Innovations

Knowing that there are physical limitations to the size of the smartphone body, there have been a few attempts to replicate DSLR quality on a smartphone.
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Writing for the website Digital Camera World, Alistair Charlton and Jon Stapley (2021) state “the fact of the matter is that smartphones have limitations" and they doubt the possibility of including "complex optics inside an object with the dimensions we expect of a smartphone.”
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The camera is one of many features a smartphone offers and while it is important to many users it has to be balanced against other features of equal or greater importance.

What are some of the ways in which image quality is being addressed in smartphone photography?

Multiple Rear Lenses.
Existing Technology.
Many smartphone manufacturers have attempted to address the issue of a true optical zoom by adding multiple rear cameras on their devices. This design feature is known as stacking and while it does address some of the issues of lossless image quality while zooming Silverberg (2021) of the BBC notes"most smartphones use a stacked system of lenses, which adds both weight and bulk, and ruins a phone's sleek design on its backside." But is this compromise worth it?
To help answer this question it helps to understand stacking a bit more. In this article, Samsung explains that the cameras operate independently but also at times together to "get a pro-level photography experience". They claim multiple cameras allow for true optical zoom, but there are limitations and this claim is debatable.
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Singh (2021) notes that "optical zoom on phones works only for a single focal length. If your phone supports 5X zoom, only 5X will be lossless. Lower and higher magnifications like 3x, 4x, 4.5X, or 6x will only be digital zoom." While this might not be significant to most users it's still an important truth to recognize when comparing the quality of a smartphone image to that of a DSLR image.

External Lenses
Existing Technology.
Lens attachments allow the user to attach a lens to their smartphone camera body much like you would attach a lens to your DSLR. The lens is separate and can be added when needed. But much like traditional lenses, they can be bulky, heavy and costly.
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Lodi (2020) writing for the New York Times' Wirecutter offers a review of some of the lenses available for smartphones (specifically the IPhone, but would work on others too).
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Her most salient point is this: “the photos aren’t always perfect, resulting in distortion, blurriness, color shifts, or all of the above, but depending on your intended use, these drawbacks may be perfectly tolerable.” In other words, at present time even the best lenses made for smartphones are a compromise to those that exist for DSLR cameras.

Liquid Crystals
Technology in Development.
One possible technology advancement as outlined in this BBC article is the use of liquid crystals to mimic optic zoom technology.
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Silverberg (2021) states "Scope Photonics has found a way to make liquid crystals "spin like tops" and reorganise themselves based on how light moves through them. The effect is to mimic a zoom lens system."
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Since this technology is still in development it can not yet be proven if this technology will rival DSLR lens optics but the technology sounds promising.
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True Optical Zoom Within the Accepted Dimensions of a Consumer Smartphone.
Technology in Development.
Burgett (2020) from the website DPREVIEW reports on Oppo's developments of a true optical zoom housed within a reasonable smartphone's body.
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At the moment this technology is still in development but would be more successful than earlier versions (such as the Samsung Galaxy S4 Zoom) which were not housed within the smartphone body and added too much bulk.