Background

Any optical experiment can be seen as a logical sequence of manipulations with light. In general, experiments include basic steps such as producing, managing, detecting, and measuring light. Let's now consider each of these steps separately and in more detail.

Light Production

We use a variety of artificial light sources to create light. Natural sunlight, flames, and sparks were used in landmark optical experiments, including research that led to Nobel Prizes, even as recently as the twentieth century. Artificial light sources can be classified based on the physical mechanisms responsible for emitting the light.

Galilean Telescope

A Galilean telescope is formed by two lenses, one of which is a converging objective lens and the second is a diverging eye-lens. The focal length of the objective lens f (1) is much greater than the focal length f (2) of the eye-lens: f (1) ≫ f (2). Additionally, the back focal point of the object lens coincides with the back focal point of the eye-lens. The ratio f (1)/f (2) determines the magnification of the telescope: M = f (1)/f (2).

A Galilean telescope forms an erect image at infinity. A comparison of the two most widely used telescopes (refracting and Galilean) is shown in the following table.

Light Illuminators

As a rule, the image produced by optical systems does not come from a self-luminous source. Objects are illuminated by light coming from light sources such as light bulbs. Of course, we can use some optics as a lens system (called a condenser) to collect light from the light source and send it in the exact direction of an object. After that, the so-called projecting optical system (lens system, mirrors, prisms, etc.) forms an image of the object. This image can be viewed on a screen or at infinity. In the following consideration, for simplicity, we will use the terms “condenser lens” to denote the optical system gathering light from the light source and “projection lens” to denote the lens system forming the image of the illuminated object on the screen. To illuminate an object, it should be placed between the condenser lens (or light source if not using a condenser) and the projection lens. The position of the object relative to both the light source and the projection lens is crucial and determines the type of illumination and magnification of the image on the screen. The most widely used schemes of illumination are described below.

Background

As was shown in Chapter 2, there are different types of light detectors: devices measuring light energy and/or power. In this and the following chapter, we consider light detectors based on semiconductors, which are very popular among researchers. In fact, semiconductor light detectors are the necessities of modern optical research life.

Semiconductor light detectors (photoconductors or photoresistors, and photodiodes) are typical quantum light sensors in which light beam energy is converted into free charge carriers generated through an internal photo-effect. The current and/or voltage due to these carriers can be measured directly. Compared to other quantum detectors, such as photomultipliers, photoresistors and photodiodes have low geometrical size and cost, are sensitive in the near UV–visible–near IR region, do not require high-voltage power supplies and, as a result, are widely used in modern research. A common (but not critical) disadvantage of all semiconductor detectors is larger noise compared to photomultipliers. If you need to detect extremely low light intensity (“photon counting”), you should use a photomultiplier instead of a semiconductor light detector. However, in real routine optical research, “photon counting” is not a common procedure (unless your research is in the field of extremely low electromagnetic fields). Semiconductor light detectors are much more practical and demonstrate excellent performance.

The measurable quantity produced by a semiconductor light detector is electric current or voltage. The dependence of such a measured electrical signal upon light power can be linear or non-linear. These two different regimes of light detector operation, namely the linear and non-linear dependence of the measured quantity (current or voltage) on the light power, will be discussed using practical examples of photoresistors and photodiodes.

Background

An ideal mirror can be defined as a surface which reflects 100 percent of the light falling on it. Mirrors can be classified depending on the shape of their reflecting surface. The most widely used mirrors are planar mirrors, spherical mirrors (concave and convex), and paraboloidal mirrors (concave and convex). Since, in the paraxial approximation, paraboloidal mirrors are governed by similar equations as spherical mirrors, let us describe spherical mirrors in more detail.

The reflecting surface of a spherical mirror has a spherical shape, which can be concave (Fig. 11.1a) or convex (Fig. 11.1b). When parallel light falls on a spherical mirror, it is reflected by the reflecting surface and converges at the focal point F as shown in Fig. 11.1.

The mirror's focal point F is located in the middle of the radius R = OV of the spherical surface of the mirror: OF = FV = OV/2. The focal length of the mirror f is the distance between the focal point and the vertex V (the vertex can be determined as an intersection point of the spherical surface and the optical axis). Therefore, the absolute value of the mirror's focal length depends on the absolute value of the radius of curvature R of the mirror surface: f = R/2.

When an illuminated object is placed in front of the spherical mirror, the mirror produces an image of the object. The type of image (real or virtual, erect or inverted, magnified or minified) and the image distance s′ (distance between the image and the mirror) depend strongly on the object distance s (distance between the object and the mirror) and the type of mirror used. The following table summarizes the imaging properties of spherical mirrors. All quantities in this table represent absolute values, i.e. they are positive.

Background

Photoconductive Mode of Photodiodes

In photoconductive mode, a diode is often reverse biased, which dramatically reduces the response time at the expense of increased noise. This increases the width of the depletion layer, which decreases the junction's capacitance, resulting in faster response times. The reverse bias induces only a small amount of current (known as saturation or back current) along its direction while the photocurrent remains virtually the same. The photocurrent is linearly proportional to the irradiance (Fig. 4.1), thereby the light detector is linear.

The photoconductive mode of a diode can be used both without an external amplifier (measured quantity – photocurrent, Fig. 4.1) and with an external operational amplifier (measured quantity – voltage, Fig. 4.2).

Semiconductor light detectors are also called “square law detectors.” This is because the probability of charge generation is proportional to the square value of the field strength of the radiation field illuminating the detector area. Table 4.1 summarizes data on semiconductor light detectors.

Background

If the axial thickness d of a lens is not neglected, we treat the lens as being a thick lens. This means that the lens thickness is comparable to the radii of curvature of its surfaces (d ≈ R 1,2). In the paraxial limit (Gaussian or first-order optics utilizing approximation sin α ≈ α), a thick lens can be described in terms of cardinal points. This description is general and can be applied to more complex optical systems consisting of different lenses.

Let us consider the thick lens shown schematically in Fig. 7.1. There are six cardinal points on the optical axis of a thick lens, from which its imaging properties can be deduced. Slightly curved surfaces (which can be considered as planes in the paraxial approximation) normal to the optical axis at cardinal points are called the cardinal planes.

The cardinal points consist of the first (front) and second (back) focal points (F1 and F2); the first (front) and second (back) principal points (H1 and H2); and the first (front) and second (back) nodal points (N1 and N2).

The first and second focal points can be defined as the images created from objects located at −∞ for F1 and +∞ for F2. In other words, paraxial rays traveling parallel to the optical axes from right to left (from left to right) are converged at the first (second) focal point (Fig. 7.1a).

The definition of the principal points can be given as follows. Let us assume that each light ray of a bundle incident on a thick lens parallel to the axis is extended to meet the backward extension of the ray after passing through the system. The principal plane can be defined as the locus of the intersection of all the rays. By definition, the first (second) principal plane is formed by rays incident on the lens from the right (left).

Background

Radiometry is a subfield of optical science dealing with methods to measure optical radiant energy. In short, radiometry deals with measurements of radiometric quantities such as radiant energy and radiant flux. The most widely used radiometric quantities and their definition are shown in Table 2 A.1, fully reproduced in this chapter.

In many practical cases, the sensitivity of the human eye should be taken into account. This can be done by considering the area of photometry. The relationships between basic radiometric and photometric units are shown in Table 2 A.1.

This chapter focuses on measurements of radiometric quantities using the simple optical detector described in Chapter 4. After completing the experimental tasks in this chapter, you will appreciate the art and science of optical radiometry and its importance to numerous applications, including the booming field of light-illuminating systems.

Unit Conversions

Radiant flux: 1 W (watt) = 683.0 lm at 555 nm

1 J (joule) = 1 W s (watt second) Luminous flux: 1 lm (lumen) = 1.464 × 10−3 W at 555 nm = 1/(4π) cd (candela) (only if isotropic) 1 lm s (lumen second) = 1 talbot (T) = 1.464 × 10−3 J at 555 nm

Procedures

Wear gloves to handle optical elements (lenses).

If you have not already done so, design an electrical circuit as shown in Fig. 13.1 to make a linear light detector (see Chapter 4 for more details).

Background

Real optical systems are always limited in size, so it is important to know how the size of an optical system affects its performance. Consider the simplest optical system composed of one thin lens, as shown in Fig. 9.1. As we increase the angle between the incident ray emitted from the on-axis point O and the optical axis, the ray will eventually hit the edge of the lens. For angles beyond this slope angle, the light rays will not be imaged by the lens. An axial ray traced near the outer edge of the system (e.g. the lens rim) is termed a marginal ray. The physical opening in an optical system that limits the amount of light that can be collected is called the aperture stop of the system (the lens rim serves as the aperture stop in Fig. 9.1). A chief ray is a ray propagating through the center of the aperture stop.

An aperture stop is a very important concept in optical system design because it determines the ability of the optical system to collect light. In other words, the aperture stop limits the brightness of the image. The image of the aperture stop, as seen from the object space (the space to the left of the first element of the optical system), is called the entrance pupil of the system. The image of the aperture stop as seen from the image space is called the exit pupil of the system. In our simple example of an aperture stop, entrance and exit pupils coincide (Fig. 9.1).

There is a simple algorithm (described below) to find the entrance pupil, the aperture stop, and the exit pupil.(1) Make images of all the optical elements of the optical system as seen from the object space.

Background

Any complicated imaging optical system is a combination of simple optical components: Mirrors, lenses, prisms, plane plates, etc. Such optical systems are described in terms of Gaussian (or first-order) optics. In general, the approach using cardinal points and cardinal planes which we used to describe thick lenses (for details see Chapter 7 of this book) is also valid for more complicated optical systems. Definitions of all cardinal points and planes are the same as for thick lenses, so we refer the reader to the previous chapter for more details. Briefly, the basic idea of the description of an optical system in terms of cardinal points is as follows: six cardinal points and corresponding cardinal planes can replace an optical system. If you know all these cardinal elements, you can make a ray tracing and build an image of any object (of course, in the paraxial approximation).

Let us consider an optical system immersed in air, as shown in Fig. 8.1. In this case, nodal (N i , i = 1, 2) and principal (H i , i = 1, 2) points coincide. Additionally, the front and back effective focal lengths are equal, so the term “effective focal length” f eff is used instead of the two terms “front and back effective focal lengths.”

The image position is found by the following useful and simple expressions:

where x 1 is the distance between the object and front (first) focal point F1, and x 2 is the distance between the image and the back (second) focal point F2 (Fig. 8.1). Distances s 1 (s 2) are measured between the object (image) and the first (second) principal plane. As seen here, these equations are similar to the equations describing a thin lens, and this fact can help one to understand the basic idea of representing the optical system by cardinal elements.

Background

A lens is used as an optical component in almost all optical devices. A lens is a piece of optical material (transparent refracting medium, for example glass or polymer; for details see Further Reading) with spherically shaped surfaces on the front and back. A ray incident on the lens refracts at the front surface, propagates through the lens, and refracts again at the rear surface (according to the basic laws of geometrical optics). Fig. re 6.1 shows a lens refracting rays from an object AB to form an image A′B′, where R 1 and R 2 are the radii of curvature of the lens surfaces, d is the lens axial thickness, n is the refractive index of the lens material, s is the object distance, and s′ is the image distance. The lens shown in Fig. 6.1 is symmetrical about a line, called the optical axis.

If the axial thickness d of a lens is small compared with the radii of curvature of its surfaces (d ≪ R 1,2), such a lens can be treated as a thin lens. Thin lenses can be converging or diverging as shown in Fig. 6.2 a,b, respectively. Converging, or positive, lenses are thicker in the middle than at the edges. Diverging, or negative, lenses are thinner in the middle than at the edges. Converging lenses cause parallel rays passing through them to bend toward one another. Diverging lenses cause parallel rays passing through them to spread as they leave the lens.

Background

Cylindrical Lenses

Cylindrical lenses (Fig. 14.1) are special types of lenses used in the field of optometry to correct astigmatism, in novel visual displays, and in many other modern optical applications. A cylindrical lens lacks rotational symmetry about its optical axis and, as a consequence, has asymmetric focusing properties. As we already know, the ideal spherical lens produces a point image of a point object (for this reason a spherical lens is said to be stigmatic). In contrast to this, a cylindrical lens produces a line image of a point object. Because of this, a cylindrical lens is astigmatic.

Consider the cross-sections of a cylindrical lens in planes XZ and YZ as shown in Fig. 14.1. The cross-section in plane YZ is rectangular, while the cross-section in plane XZ is part of a circle. These cross-sections have different imaging properties. If we consider a point light source in the XZ and YZ planes, then the XZ cross-section acts as a spherical lens (Fig. 14.2a) and the YZ cross-section as a plane parallel plate (Fig. 14.2b).

Now we understand why a cylindrical lens produces a line image of a point light source, as shown in Fig. 14.3.

It should be noted that all the equations derived for spherical lenses can also be applied to cylindrical lenses, but only for the plane cross-section (XZ shown in Fig. 14.1–14.3). With a certain degree of caution, the information you applied to spherical lenses and parallel plates can also be applied in experiments with cylindrical lenses.

The fields of optical science and engineering continue to thrive. Optical technologies have become a facet of modern society, penetrating our daily life to such an extent that even a layman, fascinated by the release of a new, colorful gadget, is convinced of the importance of optics. This same realization has occurred at the official level as well. The United Nations designated the year 2015 as The International Year of Light and Light-Based Technologies. This event made us think how we could contribute in honoring and disseminating the beauty of optics. After endless enjoyable discussions, both of us agreed that the most useful thing we could do was to provide the younger generation of optical experimentalists and novices in the field with a set of practical skills to assist in their exploration of optics.

Needless to say, this idea came to our minds a long time ago. Through our professional experience and teaching activities, we repeatedly faced the same problems while interacting with students. In short, even very knowledgeable students, who knew sign conventions perfectly and never made mistakes in their homework, suddenly became nervous in the lab as they struggled to identify basic optical components and create simple optical set-ups. Despite their theoretical knowledge, their lack of basic experimental skills made the students feel uncomfortable. We were curious why the same struggle faced all newcomers to experimental optics. Driven by our desire to find an answer to this question, we followed the universal scientific method and analyzed the existing literature. We read countless books on optics which, as we found out, all fall into two categories: theory-based textbooks and monographs, or lab manuals. It is generally believed that theory-based textbooks prepare students to later work in the lab, and any further guidance would come from lab manuals. A detailed analysis of several lab manuals which described optical experiments showed that, in many cases, the text assumes that the readers are familiar with basic concepts of experimental optics. Our daily interactions with students and with professionals from different fields, who are all trying to employ optical methods, revealed that this assumption is unfounded.

Background

Classical optical experimentalists made all their components and equipment (lenses, prisms, polarizers, mechanical holders, and even optical tables) by themselves. They spent many hours grinding and polishing a chunk of glass by hand to make a lens. As you can imagine, such an approach is time consuming and is not common today, but it brought substantial benefit to those early gurus of optics. They were able to feel, deeply and internally, all aspects of their experiments. Undoubtedly, this was one of the reasons why the classical texts on optics became classics! To familiarize you with those golden days of experimental optics, we recommend reading classical texts such as Physical Optics by Robert Wood, and Procedures in Applied Optics by John Strong. We intentionally placed these two references in the text here, instead of in the Further Reading section, to highlight the changes which experimental-based optics has made during the past few decades.

The emergence of optical companies completely changed the lives of optical scientists. Instead of polishing optical surfaces for weeks, they now bypass these hurdles by ordering required optical components from an optical company, leaving more time to concentrate on optical experiments. Knowing the optical markets and having experience in finding optical components needed is a very important skill for a modern optics researcher, not to mention that it is an important life skill in general.

As you may already know, optical companies have their own websites where information about their products is presented in a colorful way. Additionally, all optical companies print catalogs of their products which can be ordered free of charge. A researcher or optical engineer who has invested time, at least once, to study websites and catalogs of optical companies is considered to be significantly more skilled. Knowledge of the optical market is indispensable.

Background

Many optical devices (glasses, car mirrors, telescopes, projectors, etc.) can be fabricated and understood using the approach of geometrical optics. Within the approximation represented by geometrical optics, light travels in straight lines, or rays. The idea of light rays traveling in straight lines through space is accurate as long as the wavelength of the radiation is much smaller than the windows, passages, and holes that can restrict the path of the light. When this is not true, the phenomenon of diffraction must be considered, and this is the domain of physical optics.

Geometrical optics is based on three basic laws: