The focal length of a lens is the distance between its effective centre and the point at which light from infinity will be focused to a single point. The sensor of the camera needs to be positioned behind this point on what is called the image plane.
The magnification ß' of a lens describes the ratio between image size and object size and has a direct connection to the focal length f' of the lens and the working distance a. The following diagram shows how to calculate the ratio between object size, working distance and focal length of the lens.
ß' = magnification a = object distance (working distance) a' = image distance f' = image-sided focal length f = object-sided focal length F = focal point (object-sided) F' = focal point (image-sided)
The ratio between working distance, image distance and focal length is calculated as follows:
Note: for ease of use this formula is based on a thin lens and not on a complex lens system, therefore results are only approximate. As the working distance for macro, microscopy or telecentric lenses is normally fixed without focus adjustment, these lenses are not defined by their focal length, but by magnification, as this is fixed and is more helpful when selecting the correct component.
The F-number or numerical aperture defines the amount of light that can pass through the lens set-up. It is calculated by dividing the focal length of the lens by its effective aperture. Lenses are always quoted with their maximum aperture (smallest F-number) which can be reduced by closing down a diaphragm inside the lens known as an iris. The adjustable iris inside most lenses normally uses standard increments including 1.0, 1.4, 2.0, 2.8, 4, 5.6, 8, 11, 16, 22. Each increment represents a reduction in the amount of light passing through the lens by 50 %.
Depth of field (or depth of focus) is a measure of the range of object distances within which the image appears to be sharp and focused. It is a function of many things, but principally the lens iris size. The smaller the aperture, the larger is the depth of field.
Once an iris is reduced below F8.0, the sharpness of the image produced starts to be limited by diffraction. If it were not for diffraction you could reduce the iris to increase depth of focus. However, around this point the depth of field is limited by natural physical conditions. In addition it is also limited by the pixel size of the sensor, as the blur circle of the lens should not exceed the size of a pixel. For a rough estimation of the range of the depth of field, the following formula can be used:
Depth of field = 1/ß' mm where ß' (beta) = MAG = y'/y (image size / object size)
The working distance defines the free space between the object and the leading edge of the lens. Standard lenses are generally designed to focus objects ranging from infinity to a minimum object distance (MOD) in front of the lens. If the distance between lens and camera sensor is increased, the MOD can be reduced. It is possible to focus a lens closer than the MOD by using extension tubes which are positioned between the camera and the lens mount, thus increasing the flange focal length. Using this method also narrows the field of view (FOV).
The following diagram shows the effect that using an extension tube has on an image.
Extension tubes may be used with standard lenses to vary the image scale and to achieve a specific FOV, but there are a number of factors that have to be considered:
Any lens using extension tubes cannot focus to infinity
Less light reaches the sensor, as the image circle is widened and only a smaller part of the image circle is captured by the sensor
Using extension tubes results in higher magnification and a decreased depth of field
Extension tubes can be very useful, but should only be used when absolutely necessary. It is preferable to use lenses designed to work with shorter working distances and stable image quality.