Seeing lens imaging as a superposition of multiple views

Abstract

In the conventional approach to lens imaging, rays are used to map object points to image points. However, many students have a need to think of the image as a whole. To answer this need, lens imaging is reinterpreted as a superposition of sharp images from different viewpoints. These so-called elemental images are uncovered by covering the lens with a pinhole array. Rays are introduced to connect elemental images. Lens ray diagrams are constructed based on bundles of elemental images. The conventional construction method is included as a special case. The proposed approach proceeds from concrete images to abstract rays.Although the students' holistic approach seems naïve, we can find a kernel of truth in it by treating Kepler's ray drawing as an ambiguous image, see Fig. 1(c): Once we switch our attention to rays that go through a single point on the lens, we see that these rays represent a refracted camera obscura projection, cf. [22]. Thus, each point on the lens produces a whole image. Images from different points on the lens represent different views [22][23][24]. This multi-view approach allows us to take the students' preconceptions seriously: We may consider rays as connections between camera obscura images, as in Fig. 1(c).Accordingly, I will use this multi-view approach to build a bridge between the students' holistic approach and the scientists' point-to-point approach. First, I present experiments that allow students to observe the camera obscura images and their superposition. Then, I will simulate lens imaging as a superposition of multiple views. Afterwards, I introduce rays as connections between the camera obscura images. Finally, I propose a method for constructing lens ray diagrams based on these images. Observing elemental images and their superpositionEach of our eyes has a lens, so we will start with that.  Facing a varied background, hold a pen about 30 cm in front of you. Close one eye. With the other eye, try to get a sharp image of the pen and the background simultaneously. It is impossible: If the pen appears sharp, the background looks blurry, and vice versa [25].

Soft shadow images

“…In addition, the connection to their own visual experience can motivate and increase the feeling of selfefficacy. The approach of the embedded perspective can also be applied to other optical contexts such as the mirror, the lens or diffraction and can therefore also be used in optics lessons [26,[44][45][46][47][48].…”

Developing students’ ideas about lens imaging: teaching experiments with an image-based approach

“…Using the 'eye analogy', students ignore the refractive media around the eye lens [4]. If teachers use a glass lens and screen as an analogous model of the eye [8], they should point out that the glass lens represents the functions of the cornea, aqueous humor, eye lens, and vitreous humor combined.…”

“…However, this is only true for a screen in the focal plane. Thus, the misconception can be turned into an imagebased definition of the focal point, see [8].…”

“…To guide students from their holistic viewpoint to the scientists' analytic viewpoint, an image-based approach has recently been proposed [8]. It is based on whole images projected by individual lens-points.…”

“…Rays are introduced as lines connecting the object and its elemental images with each pinhole at the lens. Finally, students construct ray diagrams based on elemental images [8].…”