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I know that iPhones have great cameras but what technology underlies great phone cameras? Intuitively, the number of megapixels is only a tiny part of the story.

From wikipedia, I can see the iphone 8 for example has the following features.

8: 12 MP with six-element lens, quad-LED "True Tone" flash with Slow Sync, autofocus, IR filter, Burst mode, f/1.8 aperture, 4K video recording at 24, 30, or 60 fps or 1080p at 30 or 60 fps, slow-motion video (1080p at 120 or 240 fps, timelapse with stabilization, panorama, facial recognition, digital image stabilization, optical image stabilization 8 Plus: In addition to above: A telephoto lens with 2× optical zoom / 10× digital zoom, f/2.8 aperture. Portrait Lighting (beta)

Which ones are important for a great camera? I would guess

  • six-element lens
  • f/2.8 aperture

My ultimate intention is to find other phones which have similar spec cameras to the iphone (but cheaper).

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    Image quality may be good or bad regardless of specs. Look at reviews with sample images for the specific devices you're interested in. – xiota Nov 24 '18 at 12:38
  • The important one is the one not listed: signal-to-noise ratio at various sensitivity levels. The better the SNR the less "computational things" needed. The f/2.8 aperture isn't really important. In fact with these small sensors (and therefore short focal lengths) it is hard to get better than f/8 due to diffraction. – xenoid Nov 24 '18 at 17:54
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With phone cameras it is as much about the computational things done to it after the raw data is collected from the sensor as it is about the hardware specs. You can certainly use hardware bad enough that no amount of computational photography will overcome it. But by and large most of the hardware used in upper tier phones is good enough. It's often how that data is processed that makes one phone's images stand out over another's.

  • When you say, computational things do you mean software at the hardware level or is a custom camera app sufficient? – david_adler Nov 24 '18 at 14:58
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    "Software at the hardware level" (a/k/a firmware) is still software. It does tend to be heavily integrated with the specific hardware with which it is being coupled. In some cases the software is intelligently controlling the hardware based on the shooting conditions detected. For example, in low light the firmware may direct the hardware to take multiple frames and then use an algorithm to select the least blurry one (or combine them in some way to reduce the influence of noise, etc.). – Michael C Nov 24 '18 at 15:07
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My ultimate intention is to find other phones which have similar spec cameras to the iphone (but cheaper).

That's not too difficult. Just look for phones that use the same or similar sensors with lenses that have the same focal lengths and apertures.

iPhones have great cameras... what technology underlies great phone cameras?

What is a "great" camera?

I have a DSLR+lens combination that is amazing to shoot with. It's fast, responsive. The colors and sharpness of the images look great on the LCD screen... click... click... So satisfying... click... click...

When I finally get home, I copy the images to my computer. Then I watch as the first image loads onto the screen.... next... So disappointing... next... Focus is off... next... The colors are shifted unpredictably... next... Highlights are intermittently blown out... Doesn't matter what lens. Doesn't matter which camera body. This brand and I are simply incompatible... But it's so much fun. If image quality didn't matter, I'd use this camera all the time.

I would guess

  • six-element lens
  • f/2.8 aperture

Many specs are simply not communicated to consumers. Even if they were, interpreting them would not be straight forward.

  • Some specs cannot be compared across products because companies measure them differently.

  • Some specs are meaningless without additional information. (Like number of elements and groups in a lens.)

  • Some characteristics cannot be communicated via metric. (Like bokeh and usability.)

  • Altering some specs will affect others. Acceptable trade-offs vary by person.

Specs can help you narrow your search, but they're unlikely to tell you what you'll really want to know before purchase. Your practical options are to:

  • Rely on other people's assessments by reading reviews and asking existing owners.

  • Judge for yourself by evaluating sample images or handling the devices yourself.

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There are varying degrees of software reliance in phone cameras ... the recent "beauty filter" controversy about some current brand A phones certainly shows that their camera system relies too heavily on automatic postprocessing to be compared on hardware specs alone.

The combination of sensor size and resolution has to be right. One popular upmarket Android phone in 2018 uses a crop 6 sensor with 12 megapixel resolution, and is generally reviewed favourably. While there have been designs up to 41 megapixel at crop 4, going overboard here risks noise, slow processing, poor lowlight performance, and hitting limits of physics (go below ~1um pixel size and you hit the same limits that stop conventional microscopes from going much above 1000x magnification).

Obviously, using state of the art sensor technology (BSI, stacked sensors...) is advantageous and necessary.

A phone camera can use a non retrofocus prime lens, and due to its small size can easily use mass manufactured aspherical elements, so a huge element count should be unnecessary - however, a lot of phone cameras employ optical stabilization, which is part of the optical path.

f2.8, at the very short focal lengths in use with small sensors, certainly yields good base image quality and a lot of depth of field - it will be a much too small aperture if you want to use limited depth of field as a photographic technique without relying on postprocessing effects (fauxkeh). Some modern phones offer an alternative aperture of eg f1.5 for this reason.

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The iPhone does a lot of things such as capturing a big buffer of photos or applies a lot of post processing. I would recommend not looking at hardware specs but instead at sample shots in similar environment. You're most likely looking for very natural color reproduction and decent low light performance. The rest is subjective to your preferences. Just because they have the same spec, won't mean they produce the same images.

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