Question

Problem 8.1

Helium ion microscopy is a type of scanned-beam microscopy where patches of a sample are imaged one at a time. In other words, the pixels of the micrograph are acquired one at a time, either by moving the beam or by moving the sample. At patch (i, j), a number of helium ions with the Poisson(λ) distribution strikes the sample. For each helium ion that strikes the sample, a number of secondary electrons with the Poisson(η_i,j ) distribution is detected. The process is repeated for each (i, j) ∈ {1, 2, ..., n}² to form an n×n micrograph. All the Poisson random variables described above are mutually independent.

(a) For the moment assume the η_i,j values are known constants. What are the mean and variance of the number of detected secondary electrons at a single pixel (i, j)?

(b) Now assume that each η_i,j is independent with the uniform(1,5) distribution. What are the mean and variance of the number of detected secondary electrons at a single pixel (i, j)?

(c) Using the model from part (b), what are the mean and variance of the total number of detected secondary electrons over an entire n × n pixel data collection?

(d) For this type of microscopy, a good measure of signal-to-noise ratio is the mean number of detections divided by the standard deviation of the number of detections. What is this SNR? How does it vary with λ and n?

Answer 1

Roger's Theory- Diffusion of Innovation deals with the idea of how an innovation finds its space among the individual participants and the institutions as a whole. Roger proposes that Innovation needs four key elements or participants to influence its spread among the stakeholders. The four elements are 1. The Innovation itself: Anything that solves a human problem or reduces the effort to reach output from the input is called innovation. It can be process innovation, a service innovation or a product innovation. It is meant to reduce the effort to achieve an end result. 2. The Communication Channel: The medium of propagation of innovation is very crucial as information flow is very crucial for an innovation to propagate and increase participation and hence increase the life cycle of innovation. 3. Time: An innovation needs to pass the test of time. For a change to be accepted by all, take time and iterations. The telephone required participation from all adopters for the network to be successful and it took a fair amount of time 4. Social System: Roger's suggests that external participants such as Mass media, government regulations, and internal stakeholders' family, relationships etc. determine the social system and everyone must participate for innovations to flourish.