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.

• Gain relates the binary value reported by the camera 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

• Light source directed at the camera so 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 dark image by averaging all frames of dark movie.
• Subtract the dark image from each frame of the light movie.
• Compute the variance of each pixel (noise squared) and plot versus 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 plus the number of dark electrons plus the number of electrons gained or lost due to read noise. 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 variance of each pixel, which is equal to the noise squared. Variances of terms in a sum 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) $