The image isn't perfectly clear, because there isn't a lens barrel, we used a single lens, and moreover, the surface of the lens isn't perfectly smooth to the nano-scale. Even conventional lenses today won't be able to create a clear image with a single lens, and even traditional lenses that were designed to have smoother surfaces use special coatings to mitigate the imperfections of the surface of the lens.
As we see in the image on the left, as the lens gets pressed (as the image shifts), the image closer to the lens becomes more blurry than when the lens isn't pressed. This is because as the lens gets pressed, we figured out that the focal point becomes shorter, and if the focal point gets shorter, things behind the focal plane is going to become blurrier (or more out of focus).
From the Testing section, we were able to calculate the distance of the focal points, 30cm not pressed and 51.4cm pressed, and it can be confirmed by the images above. Although the difference is difficult to see, we are able to see that the closer object is more clear when the lens isn't pressed and the object behind is clearer when the lens is pressed.
Fixing Spherical Aberration
Spherical aberration is when the outer parts of a lens do not bring light rays into the same focus as the central part. This results in an unclear focus point and makes the image blurry. This is the main reason why the image that came out was blurry and not clear.
To fix this, from the trial and error and the research I've gone through, I came to the conclusion that increasing the size of the lens, changing the shape of the lens, and adding additional lenses will help fix the problem of spherical aberration present in the lens I created.
Problems with the jerking image
After pressing the lens and after letting go of the lens, the image jerks, and moves. This is because as the lens gets pressed, the camera sensor and the liquid lens' center don't align. To fix this problem, the new ideal model of the liquid lens I created uses a new pulling mechanism that lets the lens' center stay in place with the camera sensor. This model also lets small adjustments to the shape possible to focus on an object at any distance.