Formulas for macrophotography

Fundamentals of macrophotography

Moving the camera in closer to the subject gradually increases the size of the image on the image sensor or film, although the lens must also be extended correspondingly in order to maintain proper focus on the subject.

When the distance from the subject to the lens is twice the focal length of the lens and the lens extension is equal to the focal length, the subject and image sensor (or film) image will be opposed to each other at equal distances from the lens. Furthermore, at this very point, it will be found that the sizes of the subject and image will be equal and that the image photographed, at this time, will be "life-size" or "1:1", while the distance between the two will also be the shortest.

If the camera is moved farther in towards the subject, the image size will grow larger than the actual size, while the lens extension will also increase, and the image photographed will be "larger-than-life-size". The distance between the subject and image will also increase.

Standard 50mm lenses usually have an unassisted closest focusing distance of 45 centimeters, which is rather short. However, for obtaining still larger images near to actual size (close-ups) or for getting life-size or larger-than-life-size shots, it will be necessary to extend the lens out farther than possible with the normal built-in extension, by using extension tubes or bellows.

Scale of Reproduction

The relationship between the size of the subject and the size of the image on the image sensor or film (but not necessarily in comparison with the final photo image) is called the scale of reproduction and is usually shown as "1:1" or "1:4". In the former case, the sizes are identical or life-size, whereas, in the latter case, the image is 4X as large as the subject. Sometimes, the figures are indicated only as "1.0" or "4.0", meaning, in all cases, the size of the image.

At times, the relationship may be shown as "1X" or "4X", with the magnification showing how many times larger the image has been photographed on the image sensor or film in comparison to the subject.

The scale of reproduction or magnification is determined by the focal length and lens extension, as in the following formula :—

or, with a 100mm lens extension -

It can be seen that the scale of reproduction will increase as the lens extension is increased.

Lens Extension

Lens extension is the distance traveled by the lens from infinity for making the close-up shot, and is the amount of the built-in helical extension plus the amount of extension supplied by the bellows and/or extension tubes. Thus, if the focusing ring of the lens is set to infinity, the amount of travel supplied by the accessory will be the actual lens extension.

When the scale of reproduction is predetermined, the amount of lens extension necessary for obtaining a picture taken at the scale of reproduction will be obtained from the following formula :—

LensExtension = FocalLength X ScaleOfReproduction

or, if the scale of reproduction is "1:2" —

50 X 2 = 100mm

The lens extension for predetermined scales of reproduction, when using the 50mm lens, can be set quite simply on the Bellows Attachment, by using the scales of reproduction engraved on the rails. The formula will, thus, only be necessary when it is required to find the lens extension for scales of reproduction not engraved on the rail.

Subject Area

When the subject area, which must be photographed, for taking a picture of the pre-determined scale of reproduction must be found, this can be obtained from the following formula :—

or, if the scale of reproduction is "1:2" —

Exposure

When the lens is extended for taking close-ups, the light has to travel a greater distance than necessary when the lens is used at normal built-in extensions. Thus, the intensity of the light falling on the image sensor or film decreases and, consequently, the aperture markings are no longer correct. In other words, the exposure must be compensated or adjusted in macrophotography, i.e., increased to take into account the decrease in light.

The lens-to-image-sensor (lens-to-film) plane distance is very important for finding the exposure factor. Since the lens-to-image-sensor (lens-to-film) distance is the focal length of the lens plus the bellow extension (when the lens is used at infinity), the formula for finding the exposure factor is:

or, if the extension is 100mm —

Depth of Field

Image definition is of prime importance in close-ups and macro-shots, because the depth of field grows increasingly shallow as the lens is extended and the lens-to-subject distance shortened. Overall sharpness of the image will be possible only when the lens is focused on the correct point of focus, especially if the subject has any depth to it. The correct point of focus will be found as follows :-

Thus, if the near limit is 10mm and the far limit 15mm, the formula will give -

The lens should be stopped down as much as possible for the maximum depth of field that will be obtained and extra care must be exercised in focusing properly. On the other hand, at larger magnifications, diffraction of the light will occur when the lens diaphragm is closed down too much, resulting in a drastic fall in resolution, and, thus, it will be necessary to choose a middle course of action.