Re: [Phys-L] smartphones
Oh my, this is an amazingly complex question. I've been involved in optical
design in some fashion or other since 1978. As a result I have been amazed
at what they can do with cell phone cameras and have casually followed the
tech out of curiosity. It is impressive.
If you want to get all the details and skip this very long message, there
is one link (also listed below with annotations) that I suggest:
https://www.degruyter.com/document/doi/10.1515/aot-2021-0023/html
I've placed some links to the optical designs (including optical diagrams)
and a detailed review paper below. But first, here are some short, direct
answers to your questions.
Yes. There are multiple cameras, not just the three on the back but one on
the front. The front camera (typically for selfies) is "not as good" as the
back cameras. That's a funny statement because the front camera is quite
good compared to other cameras from just a few years ago. But, let's
concentrate on the rear cameras.
My iPhone 14 has three (main, backside) cameras, along with a flash, a 3D
point-field LIDAR, and a microphone. The three largest lenses being the
primary cameras. These are wide-angle, "standard," and 3X telephoto. On the
control panel (the phone screen) you can select which lens you want. BUT
WAIT, there are FOUR selections on my phone: wide (0.5X), standard (1X),
and telephotos (2X and 3X). What camera is the 2X? There is no 2X camera.
What they do is take the image with the 3X and 1X and then via image
processing they interpolate between the two cameras to mimic the effect of
a 2X camera without the problems of "digital zoom" which always causes a
loss of resolution. So the "fourth camera" (the 2X one) doesn't physically
exist but has an artificial resolution that is pretty impressive.
Anyway, yes, the user has to select which camera they are using.
Focal length is a funny question nowadays. Without getting into details
about principal planes, effective focal lengths, and front and rear focal
lengths, the short answer is "nearly zero." The "screen" is a semiconductor
sensor (typically a CMOS but there are other detector arrays that are very
similar that might be more familiar such as CCD arrays, the difference
doesn't matter here). Anyway, the screen is a small sensor array that is
located so close to the lens it is almost touching. If you are thinking of
a simple lens (Galilean thin lens) then, for all practical purposes the
lens is only a few tens of microns away from the screen and has a nearly
zero focal length.
More details below.
They move the lens and/or sensor array for focusing by using piezoelectric
crystals. You put a small voltage on these PZT crystals and they will
expand or contract in a very precise way. You can control the position of
the lenses (note that lenses is plural) or screen with a precision that can
be measured in nanometers. For such sophisticated lenses, you often adjust
individual lenses inside the lens stack. So it might be multiple PZT
crystals doing the job. By adjusting multiple lenses you can maintain a
better focus (including the impressive macro lens style close up focusing
that some of these do so well). The real trick is maintaining focus across
the entire screen all the way from the center (axial or meridional rays) to
the edges (skew rays). (You also need to solve the problem of chromatic
aberration across the full field as well, including while changing focus.)
You simply CANNOT do this with thin lenses and a Galilean treatment of the
optical system. All the lenses in these compact cameras are made with
aspheric surfaces. They are also made with plastic, not glass. It is much
easier to control the index of refraction with plastic formulations than
glass. Some cameras probably use GRIN lenses as well. GRIN = GRadient INdex
lenses. That is, the index of refraction is not constant across the cross
section of the lens. (If you make a flat plate with a higher index of
refraction at the center and a decreasing index towards the edges where the
index function is a parabola, you will get a remarkably good focus from a
flat plate of glass. Many laser pointers and fiber optical systems use GRIN
lenses for collimating the beam.)
There is a limit to how short a focal length you can get from a "thin"
lens. I put "thin" in quotes because no lens is thin when the focal length
is measured in microns or a millimeter or two. Think about the thin lens
equation:
1/f = 1/s + 1/s'
If you plug in f=0 then 1/f goes to infinity. Bugger, that's a problem!
Likewise, if you use the introductory physics lensmaker's equation, you
have serious problems with the radii of curvature for very short focal
lengths. The biggest issue is that your radius of curvature becomes smaller
than the diameter of the lens itself! This puts a serious limitation on the
lens size vs. focal length. Once the diameter reaches 2R then all you have
is a spherical bead.
Wheu. The answer to your question about being a single lens or a biconvex
lens is above. More directly the answer is no and neither. It is a complex
stack of asymmetrical and aspherical lenses with complex choices of indices
of refraction.
That addresses your main questions in more detail than you probably wanted.
But, here is even more detail, including optical design diagrams and photos
of the lens stacks.
This is probably one of the best and most detailed discussions of cell
phone cameras that is also generally understandable. There is a LOT of
information in this giant article. I suggest that you just skim through it
looking at the figures and images.
Note especially figures 4 (photos of actual cameras), 14 (optical diagram),
16 (standard camera vs phone camera), 17 (making the lenses smaller), 21
(exploded diagram of a typical lens stack), 24 (side-by-side images of
lenses and the associated optical diagrams), 25 (a comparison of various
lenses), 26 (the evolution of phone camera lenses in time), 34/35 (shows
the differences in wide angle vs. telephoto cell phone lenses). There are
many amazing images below figure 35. One I'll mention below.
https://www.degruyter.com/document/doi/10.1515/aot-2021-0023/html
The iPhone 15 is a whole new approach. The iPhone 15 includes prisms in
addition to lenses. This opens a whole new world of possibilities.
In the link above, look at figures 39 and 40. That is a basic right-angle
prism system that just folds the optical path. The iPhone 15 goes a step
further. They use a prism (a tetraprism to be exact) to fold the 120 mm
focal length into a very compact path. This allows them to do a 5X
telephoto lens inside a thin cell phone case. Here is a great diagram of
that path and use of the prism:
https://lensreview-en.xyz/apple-iphone-15-telephoto-lens-120mm-f2-8/
There is a nice graphic "cutaway photo" of the tetraprism partway down this
short link:
https://www.pcmag.com/news/the-iphone-15-pro-max-has-a-tetraprism-camera-what-the-heck-is-that
If all you want is diagrams to show your class, this paper (from about
2017) has a nice collection of the lens designs from their patent filings.
https://wp.optics.arizona.edu/jsasian/wp-content/uploads/sites/33/2018/11/Mobile-phone-lenses-JS.pdf
Finally, a few other items to note. These cameras also have image
stabilization systems built in to help remove your shaky hands from the
image. They also have (I think annoyingly so) built in AI systems that do
image processing to "clean up" the image you see. In some cases the AI
guesses as to what should be there and it can make some comical mistakes.
(If you expand your image to almost the pixel level you can see this in
many images, but in some cases you can see the AI even at the level of the
full image on your phone screen. This is very similar to ChatGPT's problem
of hallucination when it goes off the rails and starts guessing.)
Well, that was probably too much. Hopefully it answered your questions and
provided you with some resources you can snag images from.
John
- - - -
John E. Sohl, Ph.D.
WSU Brady Presidential Distinguished Professor Emeritus
Department of Physics and Astronomy
Department of Environmental Science
Department of Being Retired and Loving It
Weber State University
cell: (801) 476-0589 (Text me, I don't answer the phone if you are not in
my contacts.)
On Tue, Feb 27, 2024 at 10:00 AM <phys-l-request@mail.phys-l.org> wrote:
> 1. smartphones (Anthony Lapinski)
>
> I am trying to understand smartphone cameras. They used to have just one
> camera (like my current one), and now they have three. I think one is for
> wide angle, one is normal, and one is telephoto. Does the user have to
> choose one before taking a photo?
>
> Phones have a sensor to display a digital image. Is this a real image? If
> so, are the lenses in the cameras biconvex? Single lens for each camera?
>
> What are the focal lengths of these lenses? How are they able to move a
> tiny amount to focus on a variety of object distances?
>
>