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Comment on Zeiss f/0.7: You Can Now Rent Two of the Largest Aperture Lenses Ever Madeparent

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Simply put, a bigger aperture means you can let more light in, which means better image quality in low light conditions (don't need to increase film/sensor ISO level as much), and shorter minimum exposure time (for taking photos of super fast actions without blurring). It also gives you a much shallower depth of field which cannot be achieved with something of a smaller aperture.

It is of course more expensive to build a lens like this, because the larger the aperture, the larger your lens cross section has to be (to actually let the light in), and the harder it is to design such a big lens that minimizes optical aberrations. With glass, the maximum aperture size theoretically achievable is around f/0.5, anything bigger and you will have to use something with a higher index of refraction than glass. So f/0.7 is very impressive.

that minimizes optical aberrations

There is an interesting idea to simply let the lens have its aberrations and correct for them in software. i.e. customize the sensor to match the exact aberrations of the lens so the end result is normal.

You'll see synthetic depth of field effects in a lot of stock photography intended for websites. The subject is sharp and the rest of the image is blurred, like shallow depth of field but it's faked in photoshop.

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