Average Bias

As part of the start up procedure for each test, a set of unexposed raw frames were captured. These raw bias frames were used to determine the nominal offset that was subtracted from each pixel during event detection.

The algorithm used to compute the average bias image (or map) is the `mean bias clip' algorithm that J. Woo developed, which is described below:

1.

Find the median and standard deviation of every pixel through all n raw bias frames.

$$\tilde{p}(x,y)={\rm median}_n(p(x,y,n))$$ (3.1)

$$\hat{p}(x,y)=\frac{1}{N}\sum_{n=1}^{N} p(x,y,n)$$ (3.2)

$$\sigma^{2} (x,y)=\frac{1}{N-1}\sum_{n=1}^{N} \left( \hat{p}(x,y) - p(x,y,n) \right) ^2$$ (3.3)

2.

Compute the average value of every pixel, $\hat{p}(x,y)$, discarding pixels that are 3 times the standard deviation above the median value.

$${\cal{S}}(x,y) = \left\{ n : p(x,y,n) \leq \tilde{p}(x,y) + 3 \sigma(x,y) \right\}$$ (3.4)

$${\cal{N}}(x,y) = \left\{ {\rm num}(p(x,y,n)) : p(x,y,n) \leq \tilde{p}(x,y) + 3 \sigma(x,y) \right\}$$ (3.5)

$$\bar{p}(x,y) = \frac{1}{{\cal{N}}(x,y)} \sum_{n\in{\cal{S}}(x,y)} p(x,y,n)$$ (3.6)

This algorithm does a very good job at removing cosmic ray events which can be present in the bias images. It does however suffer from being computationally and memory intensive. The average bias image is written as a FITS image in READ coordinates.