## Introduction

Images of objects that fill up most of the picture frame are often called "close-ups," but that is not the subject here. This chapter is concerned with real close-ups, also known as "macro" photography. This distinction is made clear by the concept of magnification, m, which just means the ratio of the size (height) of the image of an object to the actual size (height) of the object (see Chapter 7):

imagesize object size

Standard camera lenses permit maximum magnifications of about 0.1 to 0.3 and those at the high end of this range often have a "macro" label displayed on the lens barrel, on a push button, or in an accompanying menu. True macro lenses, however, permit magnifications at least to 1.0. This is also called lifesize, 1X, or 1:1. Similarly, m = 0.5 might be denoted as 1/2X or 1:2.

The magnification concept is the key to understanding the essential features of both telescopic and close-up photography. In the photography of birds and animals, the magnification is usually quite small (m < 0.1). A lion may fill up the entire frame, but the image height will only be 24 mm or less for DSLRs and smaller cameras. In this case, the magnification is proportional to the focal length of the lens and inversely proportional to the distance from the lens to the object. This explains the need for long lenses to photograph distant animals and birds. In the absence of a long lens, the photographer has no recourse but to get closer to the subject.

At the opposite extreme, e.g., plants and insects close-up, the magnification is often 0.25 or greater. Strange as it may seem, in this situation, magnification can be increased by decreasing the focal length. This is, in fact, the effect of "close-up" supplemental lenses. The magnification can also be increased by increasing the distance from the lens to the sensor, i.e., adding extensions. These may sound like arbitrary rules, but, in fact, they follow directly from the simple conjugate equation.

Here, again, science unifies apparently disparate sets of observations, and it is worthwhile to spend a few minutes to see how everything fits together in conformity with the laws of optics. This will require a few equations. If equations are not helpful for you, please skip to the next section. For simplicity I will begin with a single thin lens (Figure 12.1), but the results can easily be generalized to compound lenses of any complexity. (Note that the right triangle formed by ends of the object and the center of the lens is similar to the right triangle formed by the ends of the image and the center of the lens. Therefore, (image height)/(object height) = q/p.)

Image

FIGURE 12.1. Magnification with a single thin lens.

As shown in Chapter 7, the working distance, p, and the image distance, q, are related to the focal length, f, by the conjugate equation:

In the telescopic limit, the object is located so far to the left that p is much greater than the focal length/ In this limit, light rays from the object form an image in the plane where q = f, and the magnification is close to 0. Now, suppose we move the object closer and closer to the lens to increase the magnification. When p = 2 f, it is easy to show with the help of Equation (12.2) that p = q and m = 1. This benchmark arrangement is shown in Figure 12.2.

Object

Object

Image

FIGURE 12.2. The arrangement for 1X magnification.

Image

### FIGURE 12.2. The arrangement for 1X magnification.

Now, suppose we need a magnification greater than 1X. One way to accomplish this is to move the object closer to the lens, so thatp < 2f. Of course, the image will not be in focus unless q can be increased to satisfy Equation 12.2. As p approaches the value off, the rays on the right-hand side become parallel, and the image plane is infinitely far from the lens (on the right). The conclusion is that the entire "macro" range (m = 1 to m = is confined between p = 2f and p = f. Of course, when p is less than f the image is virtual, and the lens functions as a magnifying glass. (Virtual means that the image appears to be where it does not actually exist, as with reflections in a mirror. A real image exists where the rays from a point on an object are brought together in another point.)

This discussion may leave the false impression that focus is always obtained by moving the lens relative to the sensor. This type of focusing, moving the entire lens unit, is known as unit focusing. The important parameter in unit focusing is the extension, or distance added between the lens and the sensor plane. Focus may also be obtained by the movement of elements inside a compound lens. For example, the front element may be moved relative to the other lens elements, which results in

p q a change in the focal length. Modern compound lenses may, in fact, use both extension and focal length change to achieve focus.

Useful expressions for the magnification can be obtained from Equation (12.2) and the definition m = q/p. For example, it is easy to show that m = —-1 . f

Therefore, in the macro range we can increase the magnification by either increasing q (the total extension) or by reducing the focal length f. In the other limit, where p is large and q/f approaches 1, the magnification vanishes.

Another useful expression for m (obtained by multiplying Equation (12.2) byp and rearranging) is m=

In the telescopic limit where p is much greater thanf we find that m = f /p This result justifies our comment that at great distances the magnification is proportional to the focal length.

Equation (12.2) appears to have all the answers, but there is a catch. Practical camera lenses are compound lenses. The object distance p is measured to the first nodal point and the image distance q is measured from the second nodal point as described in Chapter 9. Therefore, the distance from the object to the sensor is usually not equal to the sum ofp and q. Furthermore, as mentioned above, the internal movement of lens elements may change the focal length as well as the distance of the lens elements from the sensor. The bottom line is that the simple equations shown above are only useful for compound lenses when the nodal points are close together or when the locations of the nodal points are known.

Another factor that must be considered is the increase in the effective F-number, Neff, relative to the value of N, reported by the camera, that usually occurs when the magnification is increased. This, of course, can greatly increase exposure times and exacerbate the effects of diffraction. It turns out that Neff is related to the magnification m by the equation Neff = N(1 + m) except when magnification results from the use of a supplemental close-up lens. However, there is a caveat. Lenses are characterized by an entrance pupil and an exit pupil. For a symmetrical lens the entrance and exit pupils are equal, but in general they can be quite different. Typically, the entrance pupil is larger than the exit pupil for telephoto lenses, while for wide-angle lenses the exit pupil is larger than the entrance pupil. This can be verified simply by looking into a lens and estimating the apparent size of the aperture stop from the front and the rear. The pupil ratio is defined as

exit pupil entrance pupil and a more accurate equation for the effective F-number is m

So where does this leave us? The simple conjugate equation is not very useful for macro photography, the positions of the nodal points for the lens are in general not available, and the entrance and exit pupil diameters can only be estimated. (Actually, these numbers have been reported for a few prime lenses.) The situation is not ideal, but with a modern DSLR we can measure all the quantities needed for macro photography.

Consider the standard set of close-up accessories:

• Macro lens or close-focusing tele-zoom lens

• Supplemental lenses (1-50 diopter)

• Extension tubes or bellows

With a prime lens and any combination of supplemental lenses and extensions in place, the following quantities can be measured (or estimated) at close focus and far focus (^):

• Working distance, w (distance from object to front of lens combination)

• Distance from object to sensor plane, D

• Magnification, m (from measurement of image height on sensor)

• The effective F-number: Neff (from the automatic aperture setting at fixed shutter speed), and

• Resolution as a function of Neff

The attachments and relevant distances are shown in Figure 12.3.

The next few sections cover the various combinations and arrangements for increasing magnification and point out their advantages and limitations.

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