(In response to private message; but I liked the question and answer so much, I decided to share, here; I hope that's OK? It should be.)
Yes. Awesome. The correct question.
There is an easy answer, but I must digress. I have, on several occasions, happened upon wonderful books discussing, in depth, the state of knowledge of the evolution of eyes and/or light sensitivity in Animalia, and biota in general. I wish (a) I had the money to run out and purchase these crucial references... though I sometimes still remember the precise place in the stacks and the color of the binding of the book that gives the answer and sometimes I even remember the title ... and/or (b) the memory to recall what was learned in the brief time I held the book in my hands. (I probably took good notes, but my filing system precludes any reasonable retrieval. I am preparing to write a book, and have been since I left undergraduate career and began preparing for graduate school entry.).
Shorter answer? Nature does it different ways. Like twenty, or so. An awesome convergence of design principles; analogy, as a general rule, not homology (though, to be sure, there is a bit of both, if memory serves me correctly).
One thing about the computer and digital and internet revolution is the "cheapness" of thought. I am afraid I succumb to such, and your Pascal quotation is apt and diplomatic and warranted. At least I am in good company.
Similar cheapness of thought in the latter days of the printing press. All this paper and "capacity" and few scholars (due to previous century of Black Death, according to James Burke's history treating that particular subject) to fill the pages! Well, that was rectified rather quickly, with stupendous and sometimes horrifying results!
Eyes; monophyly
https://en.wikipedia.org/wiki/Eye#Evolution ;
https://en.wikipedia.org/wiki/Evolution_of_the_eye#One_origin_or_many.3FBenefits to curved image sensors? With lenses being what they are, NONE! But, if one considers lenses BEING WHAT THEY WERE, well that changes the equation.
The proper reference in this regard is Rudolf Kingslake's "A History of Lens Design", and specifically the first few chapters. It is a wonderful read, with minimal technical knowledge necessary. I will pass on a page or two, maybe on the forum (I do like my thoughts "open source"; I am coming off a recent "career"--if one calls it that-- as a "ugly-duckling-crank-scientist" (about 10 years), Scientific-radical-liberal-radio-DJ (about 2 years), and a Third-party candidate for the U.S. House of Representatives for the State of Vermont (6 months, but I didn't campaign. I thumbed to Boston, from Vermont, and went to the National archives to read the MIT Rad lab docs--from WWII--and, more to the point, the Harvard Optical Laboratory documents concerning "Fluorite Apochromatic lenses for aerial photography".), so, I am desirous of being rather "in the limelight".
I guess, what I am saying, is I like my thoughts copious, transparent, deep, unstifled, and--your point is taken--circumspect and organized. I suppose that is asking a lot of myself, and others.
I'll slow down, in the near future, as it is the holiday season, and, in any event, I must bathe and steep in the timing diagrams. I must absorb them by osmosis. And, above all, I must order a few more parts, draw a few more drawings, start plating, and etching and soldering. I gotta get something running, or it WILL BE an endless conversation, and not just SEEM like one!
Quote:
I'm not sure why it should be advantageous to have a curved imaging surface. It's what we find in eyes, but then eyes belong in sockets and like to swivel, so a more or less spherical shape is just what's needed. Of course, optics is not my speciality subject - but can you say why you believe this is a good approach?
SHORT ANSWER:
Lenses naturally produce a curved image. It took lens designers and glass chemists careful thought and attention to flatten the field (i.e. light field; the surface of optimum focus that all/most of the image points fall upon). Some tried a curved platen (cylindrical. A few tried spherical, but papers had to be specially made, so the cylinder only corrected in one direction (+/- X, but not +/- Y)). Others just lined up the subjects along a city street corner, so that the subjects, i.e. people, in the periphery were standing where the lens "wants" them to stand.
The Petzval curvature (also Coddington Curvature, though nobody calls it that, but Henry Coddington probably has priority.) and the equation describing it are intimately associated with the equations for the "aberration" of astigmatism. The Siedel aberrations is another reference you could check on wikipedia if you so desired. Correcting for curved image tends to correct for astigmatism too, but correcting for both, as I recall, is a balance of both.
Suffice it to say just about any lens purchased on the market is designed to place a flat image on a flat piece of film; and now, of course, sensors.
Is there a good reason for curved sensors? I don't know ("evolution" thinks so!). When I started the project, I planned only on a foveated (dense receptors in the central region; less dens in the periphery) imager. When I found that those existed (a 3 to 5 year journey just finding the right papers, on my own, with no graduate advisor and/or access to premium research university) I moved on to seeing if I could make them better. The photoreceptor densities then (1980s and 1990s, the papers on retinomorphic sensors were written), were not very good, and I still have yet to see one that approaches the human eye (120 million, Osterberg, circa 1930; or 94 million, Curcio et. al. circa 1990; the human eye is probably about tenfold less, as the "on-chip data compression" is substantial! hahaha! I never did find a definitive answer about "How many megapixels is the human eye" as the "apples" and "oranges" were a difficult comparison. But I collected many different data sets and normalized a few values to try to get closer to an answer.)
But before I got a good answer, suddenly the market got crazy, the pixels got small, and vision was everywhere (I graduated college in 2000, and around 2005-2010, things got really intense. CMOS helped a lot as it forced CCD, the mature technology, to compete.). So, 120 MP camera, suddenly didn't seem nuts to me. Neither did a 94 million, or 10 million.
I studied a bit about the history of motion pictures and the flicker fusion frequency (speed at which successive images will blur together and create the illusion of motion to the human eye.). So, 60 fps is a good "rule of thumb" for human vision, though 30fps, interlaced (for cathode ray tube with known phosphor "decay time") is adequate too. I think Hugh Davson's "Physiology of the Eye" cites between 40 and 50 as the fff, but, as always, his "apples" don't match your, i.e. computer science's, "oranges". The study he cites mentions all sorts of experimental conditions and anatomical "caveats".
So, not a very short answer, but, in the end, I decided it was foolish to try to planarize the foveated retina-sensor when the lens "wants" to produce a curved image in the first place. (I still might move back to planarized foveated retina sensors, but I will still need a special lens to deal with the (a) barrel/pincushion distortion, (b) Petzval curvature/Astigmatism.
Also, human optical system is (a) wide field, (b) quite sensitive (high dynamic range), and (c) variable focal length (due to flexible lens and accommodating musculature).
Besides, if curved retinas were good enough for your grandparents--and their grandparents grandparents grandparents--then why isn't it good enough for you?! Why back in Adam and Eve's day, they never heard of a flat-field lens!
As for commercial application, it probably depends on how "human" you want your Strong AI to be? Must it see like a human? Human perspective? Euclid himself wrote on issues of human "optical perspective" (i.e. Euclid's "Optics", trans. Harry Edwin Burton, Journal of Opt. Soc. Am., circa 1940s) and he didn't even have a good theory of light or images (Al Hazen is best/priority for theory of images; ancient Greeks were somewhat confused about the nature of light. David Parks wrote a nice book "Fire in the Eye" that I have been neglecting. Perhaps I'll read over the holidays?).
I was almost toying with the idea of NOT buying computer parts with the money my father was sending me. I almost was going to get one of those books I have needed for years; "Natural History of Vision" by David Wade (the scientist, not the science writer. The distinction has become one worth emphasizing, as the latter has a controversial book out, last year). I should try to be clear about light and vision, as the history and philosophy is a tangled one, and not one that seems very settled, even now. most of us just "consent" to the weird world of Einstein and Beyond (i.e. quantum physics).
Despite the ridiculous length (and near-irrelevance to my precise '816-9628-fsa project) of this, I might put this on the forum post. The method and madness and the man are one and the same. If I am going to fail in this project, I am going to do it in public. If I succeed, then others will have helped me, (clearly, as I lack any and all requisite resources.). If others succeed in doing what I have set out to do, that is OK too (but I would be a little bit disappointed). If NOBODY EVEN TRIES to do what I am trying to do here, that would be a REAL TRAGEDY!
Patent law recently changed. I almost decided to try to get a patent with my holiday money; instead of computer parts. But I think I prefer to build it; reduce to practice, rather than try to profit. That game" is a bit of a mess. Which is why I asked PandaPro to draw me a patent troll (for the Technopoly/65-0-2-opoly game). Unfortunately, his ten-year-old brain violated the copyright on the drawn examples of patent trolls that I gave him, so we will have to try to tease some more creativity out of him! hahaha!
There will be time to try for a patent later. Reduction to practice is my present mantra.
I'd love it if there were a payday in here somewhere, but there just isn't. Someday there might be; I did the "legwork" (historical, philosophical, and now, technical). But I don't see a huge commercial market for "robots" since humans are cheap and plentiful (crass, but true. I didn't invent capitalism, and I never said it was ethical, or even legal.). Perhaps, someday, the free world will prefer "guilt free" manual laborers? But Strong AI robots have rights too? Don't they?
So, what I am doing is science, not business. Short and simple. Any help you can offer, despite my endless techno-philsophical-rants, is appreciated.
And, as always, you have my promise; I will do my homework; good ideas will be incorporated into my project. I laid out my thoughts above, from the last 10 years, or so, and any ideas that come after this are some "open-source" version of yours and mine (you folks know who you are! You frequent "post-ers").
I am not prone to idle praise. I hope you know that (as I, lately, praise you folks at least once every post!).
Note: One last historical caveat. Glass history and Dartmouth Eye Institute. OK, This has to be shorter story than I can actually tell. I will have to tell it again, in another place, as it is pretty interesting. I'll just mention that G.H. Gliddon tried to make a scale model of a functioning optical apparatus of the human eye circa 1920s, at Dartmouth and U of Rochester, but for lack of suitable low-index glasses, had to scale the size up (I think it was 1.2 or 1.5 X the size of the in vivo human eye). Furthermore, I have a "just post-WWI" report that mentions that the war interrupted scientific glass supplies from abroad and that America had to ramp up research and production of such supplies for the crucial war effort. So, oddly, our country can sometimes be a little bit backwards. In our defense--as Kingslake's book mentions--the Germans (Schott, Abbe, and Zeiss) were just getting started in their science in the period of 1860-1880, and before that, optics was a bit of a scientific specialty, i.e., for telescopes. The invention of the Daguerrotype in the 1830s-1840s brought about a need for new glass and new lens design, just as the invention of the telescope had done one or two hundred years earlier (1740s, achromatic lenses, England, Chester "Charles" Moore Hall etc.).
Fascinating history! Sorry, so long! But history is a long thing!
EDIT: I'm sure a million typos above: I left them in. But one seemed "not good" to leave: "period of 1860-1880" in the paragraph directly above, not "1869-1880".
Whooops; I graduated college in 2002! (second edit!)