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c. 1878

Editor: Joe Zeligs


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abbeabbeAn apertometer is used to measure numerical aperture, abbreviated NA or n.a.   NA is the modern term which reflects the resolving power of an objective lens. In other words, the NA of a microscope objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance. The image to the left shows a later Abbe Apertometer (equipped with a single cursor) in use. A special low power objective(supplied with the Apertometer outfit, not visible in this image), is in place at the bottom of the drawtube, inside the main optical tube. In use in the traditional configuration, as shown in the image to the left, light is directed into the rounded side of the device. The light is directed through the glass slab, and is reflected up through the cover slip and then through the objective. The 45 degree angle of the back of the glass directs the light upwards. The special accessory objective at the end of the drawtube turns the drawtube itself into a microscope to view the back focal plane of the objective being studied. As the cursors are moved around the front of apertometer, their pointers will come into view. A reading is taken from the top surface scale just as the tip of each cursor pointer reaches the field, and the two readings are averaged to obtain the n.a. Most monocular microscopes of the 19th and early 20th century, regardless of maker, had a society thread at the end of the drawtube for accessories. If the drawtube was not equipped with a society thread, it would need to be adapted to accept the special objective. Today it is faster and simpler to use a Bertrand lens or a Phase telescope instead of an objective on a drawtube. The author would like to thank James Solliday for supplying the image of the apertometer on a Zeiss microscope.

abbe apertabbe apert This apertometer comes in a French Polished fitted mahogany case. The outside dimensions of the case are about 114 x 114 x 40 mm. Inside, the contacting surfaces are covered with bluish-purple felt. Inside is the instrument, two black metal cursors, and the special objective in its can. The can is lacquered brass and labeled C. ZEISS JENA on the top of the can. The bottom of the can is labeled A The lacquered brass objective is labeled Apertometer, System. and also C. ZEISS.   The objective has a fixed diaphragm on its distal end. The black cursors are made of black metal, with one curved surface which rides along the curved front surface of the apertometer and has a pointed edge, while the flat surface rides along the top, the edge indicating the reading of the n.a. when the pointer as it enters the field of aperture. The cursors are placed with their flat sides against each other, forming a 'T' to store in T-shaped compartment in the case.

The apertometer itself consists of a semicircular glass slab of known refractive index, in this case, 1.53, engraved on the glass. This low refractive index means this is the early type of Abbe apertometer made of Crown glass, and dates to before the change to Flint glass in 1880. The flat top and bottom of the slab both have a clear finish. It measures about 87 x 44.2 x 11.6 mm in greatest dimensions. The glass slab has on its flat top surface two sets of graduations, and near the flat edge at its midpoint, a small cover slip over a circular silver disk with a central round unsilvered area. The graduations closed to the round edge of the apertometer represent readings of numerical aperture, while the inner graduations represent the angle of aperture(angular aperture). When viewed through the microscope, the hole has a few pieces of silver within it making it easy to focus on the hole. The flat side of the semicircular slab opposite its curved edge is angled at 45 degrees. This serves to reflect the light entering horizontally from the curved side upward through the central part of the silvered disk.

abbe apertometer bottom The bottom of the glass slab is cemented to a brass plate with two tabs protruding towards the back, which, having squared off rather than rounded edges, allow the apertometer to be secured by a modern mechanical stage or, presumably, allow clamping to the stage of the microscope. The metal support measures about 114 x 65 mm in maximal dimensions and is about 0.5 mm thick.

light path The light path when using the apertometer is shown in the images to the left and above. Light is directed horizontally towards the curved side, and is reflected by the 45 degree angle at the back of the glass upwards through the silvered cover slip disc opening. The light source may need to be repositioned as the black cursors are moved. Using the Abbe apertometer to determine n.a. is usually reasonably accurate, provided instructions for its use are carefully followed. The instructions by Zeiss leave out a few helpful details on improving accuracy mentioned by Spitta and Hartridge. Hartridge goes further to make several suggestions for improving accuracy employing a reversed light path, with the light directed down the optical tube and the NA determined by the pattern of light falling on the front of the apertometer. Several features about Hartridge's method also make it quite tedious. Though accuracy may be slightly improved with Hartridge's method, this is not neccesary for ordinary work. The human eye cannot differentiate a change in resolution with small changes in n.a., and a satisfactory result can be obtained by
combining the instructions by Zeiss and the precautions mentioned by Spitta.

When I tested some modern objectives, the results were as follows:
In use, testing four objectives, I found the following: a 10X S-Plan Olympus objective labeled as NA of 0.30, measured an NA of 0.35. A generic 100X objective, labeled as NA of 1.3 had a measured NA using the Abbe apertometer of 1.23. Finally an apochromatic Olympus S-plan objective labeled as NA of 1.35 measured 1.30.

Outline of use:

  1. Secure the instrument on the stage
  2. Center the little coverslip under the objective
  3. With a bright light source aimed a the Apertometer's round side, more precisely center the central opening in the silver under the coverslip and focus on the edge of this silver opening, using the usual method
  4. Taking care not to disturb the focus, attach the special objective to the inside distal end of the drawtube and slide it in or out to focus on the edge of one of the black cursors.. Alternatively, use a phase telescope or Bertrand lens to do the same. This will obviate the need for using the auxilliary objective.
  5. Move the black cursor to one side and note the reading where the pointer just reaches the edge of the field; do the same in the other direction with the other cursor. Note that with this older model, with two cursors, oe has to focus on the edge of the pointer as opposed to the cross in the single cursor type shown above.
  6. The NA is the average of the two readings
  7. Note that the above can be performed with the naked eye alone with the eyepiece removed for the lower power objectives; an auxilliary magnification system is not needed for low power objectives.
  8. Note that immersion oil must be used for oil immersion objectives.
  9. Note that with the this older model with two cursors, one has to focus on the edge of the indicator.

hole of apertometerVIEW OF THE HOLE


One annoying problem I noticed in using this apertometer. The instrument tends to move when the cursor is being moved; this early version fits onto a mechanical stage clip which will prevent this. I note that in some examples, the later model of Abbe apertometer came with pins to fit in the holes on the stage (usually used for the stage clips) to prevent this annoyance. This would not be practical unless the pins were made for a specific single microscope, as most microscopes have the holes for the stage clips different distances apart and these holes are found in more than one diameter.


Although Smith, Beck, and Beck may have been the first to sell a tube apertometer in the 1860's, the Abbe Apertometer, first developed in 1871 by Abbe,was the first widely available commercial type to come into use. It was described in an article in the JRMS of 1877-8. The Abbe apertometer, was for many years, the most common form, though its design changed slightly. Although many other types of apertometer were developed, the Abbe is by far the most common form still extant today, and the later form is also the easiest to use and probably the most precise, particularly for high NA objectives. Among the other forms developed was the Cheshire Apertometer, and the Beck Apertometer.

Although the angle of aperture of ordinary objectives was sometimes measured before his time, Ernst Abbe, originator of the numerical aperture concept, made the first prototype instrument called an apertometer in 1871 and his first prototype from 1871 is part of the London Science Museum collection. That instrument was rectangular with a graduated brass plate on top. It had a prismatic piece of glass glued on to its long side. It is Bracegirdle's 39/38, inventory 1928-899 and found in section 'F' of his CD. According to Zeiss, Abbe first introduced the Numerical aperture term (NA) in 1873, and the first apertometers of the type shown here were designed by Abbe about 1876; Zeiss was apparently selling them shortly thereafter. As noted above, the first English JRMS article about this type of apertometer was not published until 1878.

Initially the glass of the apparatus(including the prototype) was made of crown glass, but by 1881, this was changed to flint glass which, having a higher refractive index, required a shorter distance between the cursors, which made it easier to use. In the JRMS of 1881, Mayall Jr. quoted the flint glass refractive index at 1.631. In reality, one modern source quotes the refractive indices for Crown glass to range from 1.52 to 1.62, and that of Flint glass to range from 1.57 to 1.75, but these overlapping values apparently do not apply to the 19th century. In fact, the glass in each Zeiss Abbe refractometer has a slightly different refractive index and each is actually engraved with the value for that particular piece of glass. This was neccesary to correctly space the calibration lines. A sampling of actual labeled values taken directly from Zeiss Abbe refractomers is: 1.53 (present example), 1.6214, 1.6233, 1.62507, and 1.62549. The illustration in the 1924 brochure and instructions for the Abbe apertometer shows an example with a refractive index of 1.62535. It would seem that most of the later examples have a refractive index over 1.62 and less than 1.63. Note below that the earliest commercial version, shown on this web page had a much lower refractive index than the others, and that it was engraved with the refractive index reported only to two decimals; this is a crown glass instrument from the very first few years of production and must date to between 1877 to 1881, since by 1881 the higher refractive index flint glass was being used for these instruments.

all abbe

The earliest commercial versions of the Abbe Apertometer had two moveable cursors and a silver disc with a small hole(figure 1); the cursors had no handles in the earliest version, but an upgraded version with a slotted base to guide the cursor was available at 1/3 higher price. The next version(figure 2) had little handles attached to each indicator, but was otherwise the same. The third version (figure 3), still had two cursors, but a slit in the disc rather than a small hole. Later, in the fourth and final form as shown in figure 4 a single cursor was provided. In the model with the two cursors, the edge of the indicator was used to determine the angle of aperture by sliding it along the curved side of the apertometer. When the indicator just barely came into view, this was the place where the reading was taken; the process was repeated on each side and the two values averaged. In the models with the single cursor, the cursor has an X on a piece of opal glass. I found the cursor type in Zeiss Catalogs starting in 1924. The double indicator type was still offered in the Zeiss catalog of 1913; therefore the change occurred sometime between 1913 and 1924. Spitta's book of 1920 still showed the double indicator type. Unfortunately I have been unable to locate any dated catalog or instruction manual containing an entry for the apertometer after 1913 and before 1924 to further narrow down the search. Since the 1920 edition of Spitta still showed the double indicator version, it is reasonable to conclude the new model with a single cursor was first produced in the 1920's. I would greatly appreciate information from anyone with catalog entries for the Abbe apertometer after 1913 and before 1924 to further narrow this down.

For many years two versions of the Abbe apertometer were offered. One simply supplied the glass and cursor(s). In those models, these parts were simply pushed along against the glass, not held in place by anything except ones fingers. The more deluxe models, had a metal base added for these parts to ride in a slot in the early models, or at the end of a spoke centered on the metal base, under the area of the coverslip in newer ones.

For the interest of the reader, Zeiss catalog entries of the Abbe apertometer are provided for 1889, 1913, and 1934. You can also see the illustration from the 2nd edition of the Zeiss instructions for the use of the Abbe apertometer.

For a discussion of the general history of the apertometer, and for other types of apertometer, please see the apertometer history page.

The author would likely to acknowledge the generous help of Dr. Joseph Zeligs and James Solliday with this web page.


  1. Carl Zeiss (company) (1924): The Abbe Apertometer Leaflet Mikro 114 (2nd ed).
  2. Gunther, N (1951) Ernst Abbe: creator of the Zeiss Foundation. Transl. by David Bower (2016) Available directly from Mr. Bower at:
  3. Hartridge H (1918) An Improved Method of ApertometryJRMS pp337-348.
  4. Ingpen, John (1878) Description of Professor Abbe's Apertometer with Instructions for its use, By Carl Zeiss of Jena. JRMS Vol I pp18-22
  5. Mayall Jr, J (1881)JRMS Ser II, Vol I, Part 2 p978
  6. Spitta, Edmund J: (1920) Microscopy. The Construction, Theory and Use of the Microscope. 3rd ed. pp94-98.