Difference between revisions of "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. (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 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) $