Microscopes Rely on Basic Optical Components

This article starts a Test & Measurement World series on the basics of optical microscopes.

C.G. Masi, Contributing Technical Editor -- Test & Measurement World, 4/1/2000

It’s difficult to determine the origins of optical microscopy. The idea that viewing objects through certain glass shapes can make them appear larger than they actually are has been around practically since people learned to make glass. It’s an effect that’s pretty hard to miss.

But understanding the effect and using it to do something worthwhile are two different matters. No one really knows who came up with the idea of using two glass lenses to make a compound microscope. Generally, people credit Antoni van Leeuwenhoek (1632–1723), a naturalist who studied biological specimens, with making the first good microscopes. Scientific historians point out, however, that Leeuwenhoek’s microscopes, although being exceptionally well made (which accounts for his fame), did not have a particularly advanced design even for the time.

A complete microscopic system needs four basic elements (Fig. 1). All microscopes start with an illumination source that bathes a sample (or specimen) in sufficient light of the correct properties (color, ray parallelism, and so on.). That light interacts with the sample before passing through an optical system (a series of lenses), that forms the heart of a microscope. The optical system creates a magnified image of the specimen, and the image then goes to the detector system, usually an eye or a camera. A mechanical stage positions the specimen in the microscope’s field of view and holds it steady.

Our goal in this Basic Microscopy Series is to help you understand how these elements work and show you how you can specify a configuration suited to your needs. We don’t intend to turn you into a microscope engineer, but we’ll help you communicate knowledgeably about microscope optics and systems.

This first installment looks at the overall optical concepts that govern the design of high-quality microscopes. Specifically, this article looks at the basic types of microscope optical systems and how they magnify an image. The next installment, scheduled for May, will look at image imperfections and how microscope designers minimize them.

Microscopes Come in Two Types
Basic optical microscopes come in two forms: simple and compound. A simple microscope has an optical system of one lens. A compound microscope incorporates two or more lenses. All the variations, such as binocular microscopes, video microscopes, and so on, are essentially modifications of these two designs.

To understand the differences between simple and compound arrangements, you’ll need to understand a few optical concepts. The first concept is index of refraction, the ratio of the speed of light in a given material to the speed of light in a vacuum. The latter property has a relative value of 1. The refractive index of air is 1.00029, which is so close to 1 that the difference is unimportant for our purposes. Different types of glass have indices of refraction in the neighborhood of 1.5 to 2.0.

Figure 1. A complete microscope system consists of an illumination source, a mechanical stage to hold a sample, an optical system, and a detector. The detector may be your eye, a photographic camera, or a video camera.

Figure 2. Light passing through an interface between materials with different indices of refraction (n) undergoes bending. The light decreases its angle of refraction when pa ssing into a medium of higher refractive index. The angle increases when the light passes into a lower-refractive-index medium.

Lenses Bend Light Rays
Generally, convex surfaces bend light toward the optical axis—an imaginary line that passes through a surface’s geometric center. Concave surfaces bend light away from the axis (Fig. 3 ). Interfaces that bend light toward the optical axis are called positive surfaces, and those that bend light away are called negative surfaces.

  When a beam of light comprising rays parallel to the optical axis passes through a convex surface, rays farther from the optical axis bend more than those closer to the axis. (Any beam made up of parallel rays is called a collimated beam.) All the rays eventually cross the optical axis, and if the surface has the right shape, they will all cross at the same point. That point is called the focus, and the distance from that point to where the optical axis pierces the surface is called the focal length. The focal length is a property of the glass-air interface, and it depends only on the lens’ surface shape and the index of refraction of the lens material.

In a microscope, however, light entering the optics doesn’t arrive in a collimated beam. Generally, the incoming beam spreads out from a sample placed relatively close to the lens. Figure 4 illustrates what happens. An image formed by the crossing of converging rays is called a real image, and the plane on which it forms is called the focal plane.

Figure 4. A convex, or positive, optical surface can concentrate rays from a source onto a real focus. The focus occurs in the focal plane.

If the lens surface bends the light enough, it will focus the beam at some distance behind the surface. That distance will be longer than the distance for focusing a collimated beam. The focal point for the optical arrangement in Figure 4 depends on the location of the source and the focal length of the surface. The relationship follows the so-called lensmaker’s formula:

where
f = the surface’s focal length
s = the distance from the source to the surface (the object distance)
i = the distance from the surface to the new focus (the image distance).

A collimated-beam represents a special case in which the source appears at infinity, so the image distance equals the focal length.

The image distance achieved by starting with a collimated beam is called the effective focal length of the lens. The focal lengths quoted for all real lenses are effective focal lengths. Don’t think of the effective focal length as an actual distance in the optical system. Instead, think of it as just the primary specification for the lens. It’s the parameter f you use in the lens-maker’s formula to calculate the actual image and object distances.

When the source distance is less than the focal length, the formula returns a negative value for the image distance, i. That means the surface curvature was not great enough to bring the rays to a real focus. The rays continue to diverge when they leave the lens, as if they came from a source further to the left in Figure 4 than the actual source. The image in such a situation is called a virtual image.

Human eyes cannot focus converging rays, they can focus only diverging rays. Thus, when you put your eye close to a lens, you see a virtual image. To view a real image, you must move your eye back past the focal plane (where the rays cross) to a point where the rays diverge again.

Use a Thin-Lens Approximation
In the rest of this article, I’ll assume lens thicknesses are much less than the source and image distances. Using a thin-lens approximation simplifies calculations and provides general dimensions for an optical system. Although this thin-lens approximation doesn’t usually hold true for microscope lenses, it lets optical designers easily start an optical design using basic assumptions about on-axis light rays. Thus, it makes it easy to illustrate basic optical principles.

Microscope lenses are complex optical structures that comprise many optical surfaces, and microscope designers have optimized the lenses to work best at a specific image distance, and in a specific, fixed arrangement. Thus, focusing a microscope usually involves moving the entire optical system relative to the sample, rather than adjusting the spaces between lenses.

Figure 5 shows three optical arrangements you can make with a single lens. Figure 5a shows a magnifier, a lens for which the object distance (s) must equal the focal length. The angular height of a magnifier expresses how to relate image size to the actual object. Angular height is actually the angle (a) the object subtends when viewed from the first surface of the lens. You can calculate the angular height from the formula

where
h = the height of the object (blue arrow)
s = the object distance

Figure 5. Lens configurations include three single-lens optical arrangements. a) In a magnifier, the source distance, s, equals the lens’ focal length. b) A telephoto lens has an object distance (s) much larger than its focal length (i). c) In a macro lens, the focal length (i), may be from one to two times the lens’ object distance (s).

Because the object distance may be very small, the angular height can be very large, even for a small object. The magnifier projects a virtual image (green arrow) of the object an infinite distance out on the source-side of the lens. The figure shows the green arrow at a finite distance from the lens because the figure has to be printed on a piece of paper. In fact, the image appears at infinity because the existing rays are parallel.

The virtual image still has the same angular height, however, which makes its apparent size appear infinitely large. Magnifiers are extremely important in microscopy—the eye lenses for all microscopes are essentially very high-quality magnifiers.

The arrangement shown in Figure 5b illustrates a telephoto lens. The object distance (s) is much larger than the image distance, or focal length (i). A telephoto lens forms an image smaller than the real object, so telephoto lenses don’t find much application in microscopes. But there is one exception—the so-called long-distance microscope. You would use such a microscope when you need to examine a small object that you can’t get close to.

A telephoto lens forms the first optical element in such a microscope. Subsequent lenses make up for the initial demagnification. Long-distance microscopes find use on production lines that do not let manufacturers place microscopes close to the objects they must inspect. These objects include PCBs that must remain on a production tray or ink-jet
cartridges that must remain in a jig.

Microscopes use what photographers call a “macro” lens, one that has an object distance (s) shorter than the focal length (i), as shown in Figure 5c. The object distance, which microscopists call the working distance, while quite short, is still longer than the lens’ focal length. This type of lens arrangement can project a real image on a camera’s detector placed in the focal plane. The camera can transmit to a display an image of magnified sample.

As in a magnifier, the angular heights of the object and image are equal, but the linear heights differ. You can rearrange the lensmaker’s formula to calculate the microscope’s magnification (the ratio of the image height to the object height):

 M = i/f –1

M = i /s

The length of the microscope’s drawtube, the housing that holds all the optical elements in place, sets the image distance (i), the distance between the lens and camera’s detector. A user focuses the microscope by moving the sample until the object distance equals the working distance. At this point, the sample appears in focus. In this type of microscope, you can increase the system’s magnification simply by extending the drawtube length, which changes the image distance.

Optics Invert Images
In Figures 5b and 5c, the images appear inverted. Directly viewing inverted images would drive most human inspectors crazy. (Modern microscopes include optical elements that produce properly oriented images for human viewing.) A simple lens can magnify no more than a few tens of times. Achieving magnifications of 100X to 1000X or greater requires using multiple lenses in a compound microscope, as shown in Figure 6 for a two-lens microscope.

Figure 6. A basic inspection microscope comprises a macro lens (objective lens) followed by a magnifier (ocular lens).

After light reflects off a sample, it goes into an objective lens that works the same way as the macro lens shown in Figure 5. The second lens, traditionally called the eyepiece, eye lens, or ocular, operates like a magnifier to let you view the image formed by the objective. Because the ocular further magnifies the magnified image provided by the objective, the total magnification for both lenses equals the product of their magnifications. Thus, if a microscope uses a 30X objective and a 20X ocular, it achieves 600X magnification.

The optical system in Figure 6 provides a virtual image that an eye can see. This optical arrangement has the advantages of being light, compact, and simple. But its image appears inverted. The objective lens inverts an image, but the ocular, a simple magnifier, does not.

Rectify an Image
To rectify, or uninvert, the image requires adding a third optical element, a positive lens that forms a real image the magnifier can deliver to an eye. This added positive lens rectifies the image and may also provide some additional magnification.

The optical arrangements in Figure 7 show how to turn the setup in Figure 6 into a compound video microscope—one that includes a camera to acquire images. The simple two-lens system (Fig. 7a) looks similar to the inspection microscope of Figure 6, except that the second lens is placed a little farther from the objective, so its object distance (s) is longer than its focal length. The second lens thus forms a real image at a distance i on the detector-array face. The height (H) of the resulting image is then Mp = i_p/s_p larger than the height of the first image. The net magnification (M) is thus

M = Mo Mp

where
Mo = the objective’s magnification
Mp = the magnification of the second lens, the projector lens.

Figure 7. You can make a simple projection microscope by moving an ocular away from the objective lens so the combination forms a real image. a) The image gets projected on a camera’s detector. b) An added third lens focuses light rays leaving the ocular.

A more sophisticated video microscope system (Fig. 7b) provides a third lens that projects the image on the camera’s detector. Because the ocular was designed to provide a virtual image at infinity, it is convenient to use a separate projection lens to focus that image onto the camera’s detector. This lens arrangement has two advantages: The camera can record the scene exactly as it appears to a user looking through the ocular, and the distance between the ocular and projector lens is not critical.

Manufacturers also offer variations on the basic compound-microscope. For example, a microscope could provide two oculars and one objective lens to let you view samples through a stereo microscope. And an added mirror could direct an image through different exit ports at the top of the microscope. By substituting a beam splitter for a mirror, the manufacturer can direct the image to two exit ports, one for optical viewing and one for a camera. Most inspection microscopes interpose mirrors between the objective and eyepiece to turn the optical path to a comfortable viewing angle. T&MW