Sizing Particles by Optical Microscopy through criteria developed by the analysis of image profiles

Abstract

Modern image analysis equipment has now made it possible to obtain detailed intensity profile information about objects imaged under the optical microscope. If the object contrast is generated by light absorption alone then the image profile of the object is a square wave and the size information is contained in the fundamental frequency of the Fourier components of that square wave. The period of the fundamental frequency lies very close to the intensity midpoint of the image profile. As long as the microscope objective numerical aperture (NA) is high enough to pass this fundamental the object can be sized to an accuracy which is chiefly dependent upon the signal to noise ratio of the system and independent of classical notions of microscope resolution. Thus for latex particle metal replicas it was possible to determine the diameter to a precision which was typically on the order of 13% of the classical Sparrow limit of resolution for the objective employed. By sizing the same particle replica with objectives of different NA it was demonstrated that the size obtained was independent of the objective NA used as long as the replica diameter was above the Sparrow limit. This is in accordance with optical theory. About mid‐summer the Goldstein "Zernike" program became available to us through the kindness of Dr. Goldstein. With this program it was possible to model the effect of optical path difference. Unlike particle replicas, most real objects generate object profiles that are a function of refractive index difference and thickness or path difference in addition to object size and transmittance. Although the "Zernike" program can accommodate path differences, it assumes that the object has negligible thickness‐an assumption not merited by most real microscopic objects. Although exact quantitative agreement could not always be obtained with reasonable assumptions, the predictions of the "Zernike" program nevertheless could help to define sample preparation conditions which enabled high accuracy sizing to be performed. This work thus demonstrates that an extremely high degree of accuracy and precision in particle sizing is available from the optical microscope which is independent of classical notions of microscope "resolution". The major requirements are that the objective NA be sufficiently high enough to pass the Fourier components which contain the size information and that features in the image can be identified which contain the size information.

Arrays of Uniform Latex Spheres as Test Objects in Optical Microscopy

“…A recent review of this method of particle size determination suggests that it is reliable to a precision of ca. 1 Yo [8]. Although the array sizing technique is generally attributed to Kubitscheck [9], it was in fact first used by Perrin in his classical studies to determine Avagado's number prior to 1910 [lo].…”