Smartphone camera design basics: Optics and form factor





By Ziv Attar



These days, smartphones come with multiple cameras, each serving a different purpose and capturing a different field of view. Take a look at any new smartphone. Each of its cameras has very different specifications.


This article explains the differences between these cameras and reveals their limitations. All cameras have certain constraints in common, but some are more specific to smartphone cameras:


Focal length - the property of the lens that dictates the camera’s field of view: the total area the camera can “see,” depending on the sensor


Aperture or F-number - indicates the size of the lens's aperture and, therefore, the amount of light that can pass through it and, among other things, defines the depth of field: the distance that is sharp around your focus point.


Dimensions - the smartphone’s lack of physical depth poses several challenges to camera design. Cost - the more lens elements, the more you pay.


Let's see how these constraints affect the different cameras in smartphones. We picked the iPhone 13 Pro as our reference.


Wide camera


The main smartphone camera. It usually has a focal length equivalent to 26 mm and a large aperture, such as F/1.5. Its sensor is 7.6x5.7 mm, so the lens's actual focal length is 5.5 mm, making the aperture 3.6 mm in diameter.


Tele camera


The tele camera has a focal length equivalent to 77 mm and an aperture of F/2.8. Its sensor is 4x3 mm, so the lens’s actual focal length is 8.8 mm, and the aperture is 3.1 mm in diameter.


Ultra-wide camera

The ultra-wide smartphone camera usually has a focal length equivalent to 13 mm and an aperture of F/1.8. On the iPhone 13 Pro, the sensor is 4x3 mm, so the actual focal length is 1.5 mm with an aperture 0.83 mm in diameter.





These camera specs raise a few questions:


Why is the sensor on the tele and ultra-wide cameras so small?


The telephoto camera has a longer focal length than the wide camera. Since the telephoto camera on iPhones is not folded, the phone's thickness limits the physical length of the lens, and the only way to give a lens a long focal length while keeping it short is by using a small sensor.


As a result, the telephoto camera sensor is 3.6 times smaller than the sensor on the wide camera. The super-wide camera has a very short focal length, so, in theory, it could use a short lens to allow for a large sensor. But in reality, a lens with such a wide field of view would require many elements and with the device’s thickness constraints, the only way to accommodate it would be to design it for a small sensor.



What happens when the telephoto camera is folded?

A folded design is one solution to removing the length constraint from the optics. The camera's long dimension must be parallel to the phone's screen, with a 45 degrees mirror added on top of the lens to ensure the camera is "looking" in the right direction.






The arrangement removes constraints on the length but adds new ones to the height of the sensor as it is no longer parallel to the screen. This new constraint still limits the sensor size but allows the lens to have a longer focal length, which is exactly what you find on some flagship Android devices.


If the focal length of the tele camera is 8.8mm and only 1.6 longer than the wide camera, why is the tele considered a 3X tele?


To understand the 3X claim, we need to look at the difference in the camera's resolution because the main objective of adding a telephoto camera is to “get closer” to the subject. Apart from focal length, the resolution depends on pixel size and the quality of the optics.


The pixel size on the wide camera is 1.9 μm, while on the tele cameras, it’s 1.0 μm. Assuming the optics can resolve such small details, the Tele camera sees a 1.9X improvement in resolution over the wide camera. Combine that with the 1.6X longer focal length, and it gives you 3X resolution in total.


Could we get 3X from the wide camera using smaller pixels and eliminate the need for a telephoto option?


That would require 0.63-micron pixels, which we can manufacture today, but we would need optics that can focus light on such small pixels to make use of them.


How well a lens can focus light on small pixels depends on the quality of the lens but can still be limited by a phenomenon called diffraction. The ability of a perfect lens to focus visible light is approximately 2.44 X wavelength X F-number. So the lower the F-number, the better the lens is at focusing light onto a small spot.


Using the wide camera at F/1.5, we see that the smallest spot a lens can form is 2 microns (we assume wavelength to be 550nm). So, using very small pixels does not provide the same zooming capability as a dedicated telephoto camera.


A wide camera can only achieve zooming results like a telephoto camera by using large pixels and a longer focal length, which is impossible with current technology. But rest assured, the team here at Glass is working on a solution.


How do the different sensor sizes and lens aperture sizes affect image quality?


Image quality is a broad term that we can break down into many parameters, such as resolution, noise, dynamic range, and color accuracy. Image quality will always benefit from more photons and a larger sensing area. Considering the sensor and aperture size and comparing the three cameras on the iPhone 12 Pro, we see that the tele has 12.5X less photon-sensing ability than the wide camera.


The ultra-wide camera has 5.8X less photon-sensing ability than the wide camera. Exposure time is another parameter that comes into play here. Generally speaking, the longer the focal length, the shorter the exposure, thus preventing handshake blur.


This puts the tele camera in a worse position than its wide counterpart. You can increase exposure time without adding handshake blur by using an optical image stabilizer or by capturing multiple fast exposures and fusing them into one image.


What did we learn from these tradeoffs?


The form factor of a camera and how it’s mounted have dramatic implications for the possible sensor size that a lens can accommodate.


The resolution or zooming ability comes at the price of using small pixels.


When using traditional camera technology that has been around for 200 years, we can’t overcome limitations introduced by form factor, and the compromises made in smartphones today are inevitable.