Tech Notes

Determining the Theoretical Resolution of Infinity Instruments

Infinity instruments operate at extraordinarily long working distances, yet provide resolution equal to—or better than—instruments which function much closer. Most Infinity Instruments incorporate internal focusing;  working distances range considerably. In order to determine the theoretical resolving power, it is best to use a formula which works for any distance selected. Abbe provided the concept of numerical aperture (N.A.):

1. Divide the radius of the objective by the working distance (in mm). This provides the tangent. Consulting mathematical tables or calculators for the sine of this tangent will provide the exact N.A.
2. Multiply N.A. by 3,000 (Lord Rayleigh's formula) to get the theoretical resolution in lines/mm (LPM).
3. By dividing LPM into 1,000 (there are 1,000um per mm), you will arrive at the theoretical resolution in um (microns).

For example: The CF-Series objectives for Model K2/S have apertures of 38mm (with the exceptions of CF-4 has 20mm aperture). The radius is therefore 19mm. Assume that the CF-2 objective is used at 166mm working distance from the lens' front surface. 19/166 = 0.114 N.A. Consequently multiplying 0.114 by 3,000 = 342 LPM. Dividing 1,000 by 342 = 2.92um theoretical resolving power.

The diameters/radii of Infinity instruments are:

• Model InfiniVar CFM-2/S: 8.5mm/4.25mm
• Model K2/S / Model KV/S: 38mm/19mm (CF-4 = 20mm/10mm)
• InfiniMax/S: 30mm/15mm
• InFocus Model KC/S (Direct and with IF-Series Objectives): 20mm/10mm
• InFocus Model KC/S and InfiniTube Series (with Infinity-corrected Microscope Objectives): Limited only by the quality and N.A. rating (usually engraved on the objective). Since the Model KC/S is then "a microscope stand in a tube," it can be used to the theoretical limits of optical microscopy.

Although it is possible to take the extra step to consult mathematical tables or a calculator for the exact N.A, it will usually not be necessary, since tangent and sine are virtually identical at the numerical apertures at which Infinity instruments operate.