Scanning microdensitometry of objects small relative to the wavelength of light

Abstract

Diffraction effects may have to be taken into account in microdensitometry when dealing with relatively dark specimens even an order of magnitude larger than the wavelength of light, and become progressively more important with smaller objects. According to geometrical optical theory, when scanning across the straight edge of a uniformly absorbing, semi-infinite object the distribution error per scan line is directly proportional to the diameter of the measuring-spot. Diffraction theory predicts similar results for measuring-spots larger than about 3 times the wavelength of light, but a significant error per scan line with very small or even infinitesimal measuring-spots. Diffraction theory further indicates that point absorbance measurements can be 95 + % accurate in the centers of 6.25, 2.5, and 2.0 microns diameter disks with absorbances respectively up to about 1.0, 0.39, and 0.25, but that this accuracy is unattainable with any object less than 1.25 microns in diameter. Scanning, integrating absorbance measurements are of somewhat lower accuracy than central point measurements with relatively large objects, e.g., they are only about 89% accurate with a 6 micron diameter object of absorbance 1.0. With very small objects, diffraction theory shows distribution error to be almost independent of the size of the scanning spot, and with an object of less than about 0.125 micron diameter the apparent integrated absorbance predicted by diffraction theory is effectively identical with that predicted by geometrical theory for an infinitesimal object scanned with a finite measuring-spot, i.e., it is the product of the object area and 0.4343 (1-It), where It is the true transmission. Scanning microdensitometry of objects of very low true absorbance is effectively free from distribution error. In practice, distribution error can be reduced by using an off-peak wavelength, by reducing the area illuminated, and by routine measurement and offsetting of apparent glare (some of which is actually due to diffraction). Little or nothing is to be gained by using a measuring-spot smaller than about one-quarter the wavelength of light.