1.

Introduction (Purposes, Related literature, related methods; outline of paper)

Our objective is to introduce students to lens imaging in the context of optical image processing. In addition students are introduced to light scattering (clean glass versus translucent tape), point sources. Better students discover basic ideas about depth of focus as influenced by aperture diameter. The experiments described were created for use in a laboratory-based holography-centered introductory optics course serving a mixture of physics, chemistry, and science education sophomores and juniors. The experimental apparatus and experimental procedures described introducing lens imaging in the context of optical image processing. The author believes the apparatus and procedures described are simpler than any described elsewhere. Because of this simplicity, they can be used with almost no previous experience with lens imagine. Despite this simplicity, they seem very effective as an introduction to optical image processing.

Optical image processing is introduced in most sophomore-junior level optics texts¹. A second source of information on optical image processing and optical diffraction is a set of lab experiments authored by Arthur Eisenkraft, and distributed for many years by the Metrologic Corporation. These materials are still available through the company Industrial Fiber Optics². A very attractive apparatus for teaching optical image processing is the house diffraction plate, an apparatus created by Ronald Bergsten, at the University of Wisconsin, Whitewater. The Bergsten diffraction plate is based on a diffractive method of color imaging first described by J. D. Armitage and A. W. Lohmann³. Our method is simpler to implement than any of the previously described methods. Also, since it uses zero-order laser light, and no diffraction grating, it is easier for the beginning optics student to grasp. In previous experiments, the distinction is between low-spatial frequency and high-spatial frequency diffraction gratings. In our method, the distinction emphasized is between scattered laser light (spatially incoherent laser light) and non-scattered spatially coherent laser light. The objects utilized are microscope slides with attached opaque letters, and Scotch Magic™ tape. A razor blade or thumbtack serves well filter. The manipulations are not ‘critical’ or stressful.

The experimental arrangements, and the basic phenomena, are described in some detail in Section 2. In Section 3 diagrams that are useful for interpreting the results are discussed. In Section 4 comments are made on how this apparatus relates to previous experiments, and how the objects described in this report might be further elaborated.

2.

Experimental procedures and results

2.1.

Objects used

In Figures 1 and 2 examples of objects used are shown. Figure 1 shows the word ALE affixed to a 25 mm by 75 mm microscope slide. The three letters are formed by opaque stick-on (or dry-transfer) figures. Words containing a ‘pointing’ letter, like the letter A, work well to highlight when an image has, or has not, been inverted. In our experiments two of the letters had a translucent surround, and one had a transparent surround⁴. The translucent surround was fabricated by covering the letters L and E, and the surrounding region, with Scotch MAGIC^TM tape. See the L and the E in Fig. 1 and the W and the G in Fig. 2, as examples. However, the letter ‘A’ had a transparent surround. The transparent surround was arranged simply by placing no tape over the letter or its surrounding region, and by keeping the glass clean, to minimize light scattering. See the letter ‘A’, in ALE in Fig. 1 and the letter ‘A’ in WAG, in Fig 2, as examples.

Figure 1

An example of a translucent-transparent object.

Fig 2.

Photograph of the back-lighted translucent-transparent object shown on right.

The strong scattering characteristic of the Scotch MAGIC™ tape, and the lack of scattering by the clean microscope slide, are demonstrated in Fig. 2. A photograph is shown of a back-lighted transparent-translucent microscope slide, bearing the three figures W, A and G, formed by placing a camera at a slightly off-axis location. The letters with a translucent surround are highly visible, while, in a darkened room, the letter “A,” which has a transparent surround, has low visibility.

2.2.

Experimental arrangement

Figure 3, below, shows the basic experimental arrangement. For clarity, the system is shown twice in Fig. 3. In 3a), the light rays that have been scattered by the translucent tape on the microscope slide are emphasized. In 3b the light rays that pass through the transparent regions of the slide are emphasized.

Figure 3.

Translucent light rays (3a) and transparent light rays (3b) are shown. Both types of rays transit the system simultaneously. For the purpose of clarity, two drawings are introduced.

Legend:

• 1. Laser beam

• 2. Relay mirror

• 3. Screen

• 4. 20 cm focal length image forming lens

• 5. Microscope objective lens

We will refer to light that has been scattered by the translucent tape as “translucent light.” We will refer to light that has not been scattered by its passage through the microscope slide as “transparent light,” because it has passed through one of the transparent regions of the microscope slides.

Two different object distances are involved in this optical system. The point source of the transparent light is at a different distance from the lens than the point sources of the translucent light. In Fig. 3, the point source of the transparent light is the focal point (F_mo’) of the beam spreading microscope objective lens. F_mo’ might be d_{o, tsp} = 60 cm from the image forming lens (or usually even more). In contrast, the point sources of the translucent light are distributed over the surface of the tape that covers portions of the microscope slide. The tape is two focal lengths (d_{o, tsl} = 40 cm) from the 20 cm focal length image forming lens. We might think of the translucent tape as consisting of a large number of tiny “point-sized” randomly oriented and randomly sized prisms, Each of these tiny prisms directs its portion of the incident light in a different direction. Thus each part of the tape sends light out in all directions (like a tiny pinhole), but accomplishes this without absorbing or blocking much of the light.

Because there are two different object planes, one at 60 cm and one at 40 cm from the imaging lens, there are also two different conjugate planes.

• • for the translucent light:

  • ○ The object plane is the surface of the translucent scattering tape, at d_{o, tsl} = 40 cm⁵.

  • ○ The conjugate image plane is at d_{i, tsl} = 40 cm. This assumes a converging imaging lens with a focal length of 20 cm.

• • for the transparent light:

  • ○ The object plane is at the focal point of the beam spreading microscope objective lens, d_{o, tsp} = 60 cm from the imaging lens in our example. This is the point F_mo’ in Fig. 3b.

  • ○ The conjugate image plane is at d_i,tsl = +15 cm, in our example. This is Point P’ in fig. 3b.

Students perform this experiment twice, first back-lighting the object with parallel rays from a laser collimator, and second for a situation like that shown in Fig. 3, with the point source of the spatially coherent laser light at a non-infinite distance from the imaging lens (d_{o, tsp} = +60 cm in our example). When the laser point source is at infinity (collimated laser beam), the conjugate image plane for the transparent light is at the imaging lens focal length, i.e. at 20 cm in our example. On the other hand, if the point source of the laser beam is moved closer to the imaging lens (to d_{o, tsp} = 60 cm in our example), then the conjugate image plane moves further from the imaging lens, to a distance greater than 20 cm (to d_{i, tsp} = 30 cm in our example).

2.3.

Phenomena observed

This relatively simple experimental arrangement provides a rich environment for exploration. Two main types of phenomena observed are shown in Figure 4 and in Figure 5.

Figure 4.

Optical image processing in action.

Figure 5.

Transparent (unscattered) light is shown for the case of a collimated laser beam backlighting the object. The shadow of the opaque figure A is visible on a sheet of white paper placed anywhere between the microscope slide and the lens, and also anywhere between the lens and the viewing screen.

Figure 4 (below) shows optical image processing in action.

• • Case 1. Images of all three letters A, L and E are seen on a screen 40 cm past the imaging lens. In Fig. 4a, the razor blade is not utilized, and none of the light passing through the imaging lens is blocked. A clearly resolved image of the letters L and E results. These are focused images formed by translucent light, on a screen at 40 cm from the imaging lens. Also, an image of the letter A appears.

• • Case 2. The image of the letter A is blocked/filtered. Images of L and E are seen. In Fig. 4b, the razor blade metal acts as a blocking filter for transparent light. At the same time, most of the translucent light passes around the razor blade. The clearly resolved images of the letters L and E, formed by translucent light, are seen on a screen 40 cm from the imaging lens. However, the transparent light is blocked if any small opaque object is placed at P’ in Fig. 3b. The letter A does not appear. The region on the viewing screen surrounding the ‘black letter A’ turns dark, making the image of the ‘black letter A’ not visible.

• • Case 3. The image of the letter A is passed; the images of L and E are blocked. In Fig. 4c, the small hole in the razor blade is placed at Point P’ in Fig. 3b, and this hole passes most of the transparent light. The solid part of the razor blade is extended by black construction paper, causing most of the translucent light leaving the imaging lens to be blocked. Only the image of the letter A appears on the screen.

Figure 5 shows another dramatic phenomena, which quickly catches student’s attention. Students see that the image of the letter A appears everywhere past the imaging screen.

3.

Ray models and discussion questions

Figure 5 serves both to describe an important observation, but also helps to explain this phenomena (the letter A is visible at many view screen locations). A main question then arises: Why is the letter A visible at essentially all locations of a screen, while the L and the E form clear images only for a very narrow range of screen locations. To move the discussion forward, a diagram like that shown in Fig. 6 can be introduced.

Fig. 6.

Translucent light, i.e. light scattered from translucent “Magic” Scotch tape is emphasized. Transparent light is omitted from this diagram.

For a person experienced in optics, the theory underlying the formation of the focused image, as depicted in Fig. 6, should be familiar, and will not be discussed in detail here. We simply note that the quantitative part of the image location involves only the lens image position equation (1/do + 1/di = 1/f). The image size is treated by the lateral magnification equation m = hi/ho = (-1)(di/do). The theory of ‘depth of focus’ can also be introduced, because it comes natural to try to explain why the screen position has some tolerance for error, which forming the positions of the L and the E. However, the ‘image’ formed by the light passing through the transparent surround of the letter A, in ALE, for example, is not a conventional focused image. Explaining the behavior of the image of the letter A, and putting it in a proper perspective can challenge even the experienced student of optics.

In this author’s opinion, one should avoid stating that the image of A is always ‘in focus.’ The image of the letter A is not a focused image. Focused images, both real and virtual have, as a main characteristic, that they have a definite location. The letter A, in the example being discussed, does not have a restricted image location. It is not a focused image of the type usually encountered in beginning imaging experiments.

Rather, what appears to be an image of the letter A is, in fact a ‘shadow’ analogous to the shadowing action of a pinhole in a pinhole camera. The opaque letter A, affixed to the microscope slide, and back-lighted with laser light is like a large aperture ‘pinstop’ camera. The shadow formed by the opaque letter A is carried wherever the transparent rays go, and so, quite dramatically, appears on a white sheet of paper moved to various locations on either side of the imaging lens. A dramatic indication of the presence of diffraction around the edges of the opaque letter A shows up on the screen in an experiment like that depicted in Figure 4b, if the transparent light is blocked by a push pin, rather than by a razor blade. Then the edge diffracted light is not focused into the same small region as the undiffracted light, and this edge diffracted light is not blocked by the push pin. Then, the shape of the letter A is outlined by a thin red line. In traditional optical image processing, this is regarded as a demonstration of ‘optical differentiation.’

Several specific discussion questions have been formulated and presented to students to stimulate them to develop their thinking about the observed phenomena. Several are listed next, with brief answers.

4.

Conclusions

These experiments are a fun way to get started with imaging, and optical image processing. However, they are challenging for some beginning students. The next time I teach this experiment, I will try breaking the experiment down into three separate parts. 1. Give students a microscope slide having three opaque letters, and no translucent tape. 2. Give students a slide with three opaque letters, with all surrounding regions covered by tape. (No transparent light.) 3. Give students the translucent-transparent object, like those shown in Figures 1 and 2.

To further elaborate the object, it is very attractive to then proceed to the introduction of weak holographically formed diffraction gratings, for example with vertically spaced lines, to serve as a surround for the opaque letters. This would move these experiments in the direction of more traditional optical image processing experiments. Additional interesting filtering operations would become available, and this object could be used to introduce the basic properties of non-focusing diffraction gratings.

Another interesting variation would be to replace the opaque ‘A’ with transparent surround. Instead make the surround opaque, and the letter A, itself, transparent. The figure A would then more obviously resemble the hole in a pinhole camera.

Because my optics course emphasizes holography, I require students to form records on holographic film of their processed images. Thus familiarizes students with film handling, and film chemical processing. Also students are sometimes surprised to see characteristics of the light pattern recorded in the film that they had not noticed while looking directly at the light beams. I would appreciate receiving feedback from anyone who tries this type of experiment.