Professor Newman…
Professor Newman looks into the notion of ‘telephoto’ lenses
In my previous article, I discussed the impact of designing glass elements into phone camera lenses.
Here I’ll look at another phone lens conundrum, that of ‘telephoto’ lenses.
Again, we start with the absolute limit on a lens’s resolution capability, which is the diffraction limit provided by the 5mm entrance pupil (aperture) diameter, that’s dictated by the slimness requirements of a phone. The angular resolution limit of 0.008° is calculated from that entrance pupil and the wavelength of the visible light. In practice, the smallest total angle of view from such a lens is about 10° if we want to produce 1k pixel image, regardless of sensor size. This corresponds to a ‘full-frame’ focal length of 200mm, which is usefully ‘long’, but not ever going to pull in distant subjects. This limitation is given entirely by the aperture size of the lens.
So, let’s now look at two different design solutions to providing ‘200mm equivalent’ capability in a mobile phone. The first is simply to use a very small image sensor behind the lens. Pixel sizes of around 1.3 microns can produce very good results with modern technology, and a 1k sensor so equipped would end up at about 1.3mm across, which in sensor size terminology is ‘type 1/10’. The focal length needed to produce a 10° angle-of-view on such a sensor is 7.4mm, which could be fitted within the space limits available. Incidentally, this lens would have an f-number of 1.5, which is quite feasible for a well-corrected lens.
Solution two is to use a ‘periscope’ lens, in which a mirror or prism behind the front element(s) of the lens turns the rest of the lens through 90° so that it lies sideways within the phone. Notice that it does not allow for a larger entrance pupil, since its size is limited by the prism/mirror, which in turn is dictated by the slimness requirement. But the periscope design does allow a longer lens structure, so a larger sensor might be specified. Suppose a ‘type 1/2.4’ sensor, 6mm across, is to be used. To give 10° angle of view a focal length of 34mm is required, which can be packed into the periscope tube. The lens will have an f-number of 6.8.
In optical terms, neither solution is better than the other. Both collect the same amount of light from the same angle of view, and use the same angular sampling rate. Which is better comes down
