Relationship between image contrast and electron dose

As a means of offering more background on my radiation damage study, this quick post will highlight some relevant information from the paper Experimental high-resolution electron microscopy of polymers by David C. Martin and Edwin L. Thomas.

The main takeaway is that high resolution electron microscopy of organic materials is limited because of their sensitivity to radiation damage. In order to understand the relationship between image contrast and radiation damage more quantitatively, let us take a look at a few simple equations. The number of electrons Q which are incident on an area d² is

where J is the total electron dose (electrons per unit of area) and d is the smallest resolvable feature size of the object of interest. Since the standard deviation in the intensity of an object illuminated with Q electrons is the square root of Q (this is simply the square root of the variance, which is the number of electrons Q), the noise of an electron microscopy image is given by

From this equation we can see that the noise is minimized as the electron dose J is increased – and herein lies our problem. Since organic materials, such as the polymers that I am studying, are especially sensitive to radiation damage, my current goal is to determine a critical electron dose at which high contrast can be achieved without destroying the material’s structure.

According to this paper, the critical dose J_c can be obtained by fitting the intensity of diffraction peaks as a function of electron dose to the following exponential function:

Thus, as explained in my research update post, the critical dose can be obtained by taking the inverse of the decay rate. As for the extra background intensity term, I am still working on whether that should be included in the fit because I’m not sure if I can assume the decay goes to zero.