# Manta G032 camera measurements

## Overview

This page contains data from the demo I did in lecture on 9/22/2015 of the Manta. The point of the demo was to measure the gain $ g $, dark current $ i_d $, and read noise $ N_r $ of the Manta G032 cameras we use in the microscopy lab. Note that I showed a linear plot in lecture and the plot below is log-log.

- Gain relates the binary value reported by the camera, referred to here as
*counts*, to the number of electrons collected in a pixel: $ P_{x,y}=g N_{x,y} $, where $ P_{x,y} $ is the value reported by the camera at pixel location $ x $, $ y $, and $ N_{x,y} $ is the number of electrons detected. - Dark current is the average number of dark electrons that are collected in units of electrons per second.
- Read noise is a roughly Gaussian distributed random variable that lumps together noise sources that arise when counting electrons.

## Measurement procedure

- Direct a light source at the camera to produce a range of intensities on the surface of the detector.
- Record a 100 frame movie of the light source at 20 FPS with an exposure of 150 μs.
- Turn off the light source and record a 100 frame dark movie with identical exposure settings.
- Compute a single, average dark image by averaging all frames of the dark movie.
- Subtract the dark image from each frame of the light movie.
- Compute the variance of each pixel (noise squared) and plot versus the average value (signal).

## Calculations

The value of a particular pixel over a certain time interval, $ P_{x,y}[t] $, is equal to the sum of the number of photoelectrons and the number of dark electrons counted during that interval plus the number of electrons gained or lost due to read noise, times the gain $ g $. (The square brackets indicate that $ P_{x,y} $ is evaluated at discrete time points.) Mathematically:

- $ P_{x,y}[t]=g \left(I_{x,y}[t]+R_{x,y}[t]+D_{x,y}(t)) \right) $,

where

- $ I_{x,y}[t] $ is the number of photoelectrons generated during interval $ t $,
- $ R_{x,y}[t] $ is the read noise during time interval $ t $,
- and $ D_{x,y}[t] $ is the number of dark current electrons generated during time interval $ t $.

The next step is to write an expression for the mean value of each pixel. Means of terms in a sum add, so $ \langle (P_{x,y}) \rangle $ can be found by summing the means of the three individual terms. The mean value of read noise is zero, and the mean value of dark current is $ i_d \delta t $, which gives:

- $ \langle P_{x,y}\rangle = g\left(\langle I_{x,y}\rangle + i_d \delta t \right) $

We subtracted the average dark frame to remove $ i_d \delta t $, so the value plotted on the horizontal axis is just $ g\left(\langle I_{x,y}\rangle \right) $. Cool.

Now we need an expression for the noise. Variances of a sum of terms also add, so $ \operatorname{Var}(P_{x,y}) $ can be found by summing the variances of the three individual terms. The photoelectron count, $ I_{x,y} $, is Poisson distributed, so its variance is equal to its mean: $ \operatorname{Var}(I_{x,y})=\langle I_{x,y} \rangle $. The second term has a constant variance that is a property of the camera, the read noise $ N_r $. The third term is also Poisson distributed, with an average value of $ i_d \delta t $, where $ \delta t $ is the exposure time. This gives:

- $ \text{Var}\left(P_{x,y}\right)=g\left(\langle I_{x,y}\rangle+N_r^2 + i_d \delta t \right) $

The x-intercept is equal to read noise plus dark noise times $ g $. The slope of the line is equal to $ g $.

## Results

The slope of the line, $ g $, is equal to 0.2987, meaning that the camera produces approximately 1 count per 3.3 electrons.

The intercept is around 15 counts, meaning that dark plus read noise is about $ \sqrt{15}=3.9 $ counts, or about 13 electrons at this (short) exposure time.

I took another dataset with a 1 second exposure so we can to figure out the relative contributions of dark and read noise. I will post soon.

For comparison, the Orca Flash 4.0 scientific CMOS camera has a read noise of 1.6 electrons and a dark current of 0.06 electrons per second (with air cooling). The Flash 4.0 cools its detector to achieve such a low dark current. The camera also provides a slow-readout mode in which the read noise is reduced to 1.4 electrons. The gain of the Flash 4.0 is 2.