Once a photomicrograph is produced, one may desire to know some basic information regarding it; for example the scale of reproduction, or degree of magnification. To calculate most information only a little simple math is required. The formula for determining the scale of reproduction when using a camera with an integral-lens as follows:
Scale of reproduction = Objective magnification x Eyepiece magnification x Focal length of lens / 250
The formula works because the product of objective and eyepiece provides the initial base magnification, while the second portion of the equation provides the degree of reduction effected by the cameras optics. The lens will provide some level of reduction, unless it has a focal length equal to or greater than 250mm, which is expressed as the quotient of its focal length (in millimeters) and 250. The divisor in this case comes from the distance at which the virtual image is produced by the microscope expressed in millimeters.
The authors lens has a fixed focal length of 55mm, (which will provide a reduction of approximately 1/5) meaning that a 10x objective and ocular will produce a photomicrograph presenting with a magnification of 22x. To determine the accuracy of the calculation [or when using cameras with lenses of unknown focal length] one may measure the field of view visually with a stage micrometer (in this case measured at 150μ), and again as reproduced on the photomicrograph (measured at 63μ) and calculate the practical factor of reduction or effective magnification of the photomicrograph (23x which bears out the accuracy of the previous calculation).
Many consumer digital camera carry a lens with a variable focal length of from 2-25mm and this may be set by the user in manual mode, or determined after the fact by reading the exif data of the digital image.
For most focal lengths one will discover that the entire photosensitive surface is filled, be it 35mm film or a digital sensor. As a result only a portion of the microscopes field of view will be recorded. This effect will surprise some technicians who may expect to capture photomicrographs that are circular, just as the field of view is. Theoretically, to capture a more complete image of the field of view presented by the eyepiece, one may employ a lens having a shorter focal length. To determine the lens focal length that will provide the ability to capture the entire field of view one must know the nominal size of the field of view provided by the microscope eyepiece in use as well as the size of the imaging surface.
The rectangular sensor of the authors Nikon 1 J1 digital camera is 13.2mm by 8.8mm giving it a hypotenuse of 15.8mm. To entirely fill the sensor area, and produce a rectangular photomicrograph, while still imaging the largest portion of the field one will use the sensors longest dimension in the following formula. To image the majority of the field use the smallest dimension. The field of view index may be determined in a general way by measuring the field diaphragm of the ocular employed, it may be inscribed on modern oculars as a number following the inscribed power.
The imaged areas hypotenuse is equal to the sensors hypotenuse divided by the index of the field of view provided by the eyepiece.
Sensor dimension / Field of view index = Visible image diameter
This equation should well illustrate that a significant change in the scale of reproduction as effected by the cameras lens, will in essence, spread the photosensitive surface over a larger portion of the field of view. Doing so, will serve to reduce the resolution of the photomicrograph. So it is best then to use the above equation only to describe the power of magnification inherent in the image. With the above information one may mark a photomicrograph with a line and appropriately label its length with ease. Micrographs are best provided with this marking as it then acurately provides information on the size of imaged structures and magnification independent of the size at which the image is produced as a print.
Suffice to say that if one desires to image the whole of the visual field without introducing significant aberration or image degradation the simplest and best method is to operate a camera with a very large photosensitive area. One may consider that most of the historic photomicrographs (especially those presenting a circular field) were produced on plates or films considerably larger than 2.25 by 3.25 inches which is quite a bit larger than most widely available film or digital sensors.
What is the take away from all of this? Consider alternatives to the use of an integral-lens camera if one needs to produce an image having particular magnification or field coverage. Use the above to determine the characteristics of the photomicrographs one does produce and strive to take superior images with the equipment one possesses.