Difference between revisions of "Manta G032 camera measurements"
From Course Wiki
| Line 2: | Line 2: | ||
==Overview== | ==Overview== | ||
| − | This page contains data from the demo I did in lecture on 9/22/2015 of the Manta G032 | + | 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 <math>g</math>, dark current <math>i_d</math>, and read noise <math>N_r</math> 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: <math>P_{x,y}=g I_{x,y}</math>, where <math>P_{x,y}</math> is the number of counts measured at pixel location <math>x</math>, <math>y</math>. | |
| + | * 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== | ==Measurement procedure== | ||
| − | * Light source directed at the camera so to produce a range of intensities | + | * Light source directed at the camera so to produce a range of intensities on the surface of the detector |
| − | * 100 frame movie | + | * Record a 100 frame movie of the light source at 20 FPS with an exposure of 150 μs. |
| − | * 100 frame dark movie | + | * 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== | ==Calculations== | ||
| − | The | + | The value of a particular pixel over a certain time interval, <math>P_{x,y}[t]</math>, 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: |
:<math>P_{x,y}[t]=g \left(I_{x,y}[t]+R_{x,y}[t]+D_{x,y}(t)) \right)</math>, | :<math>P_{x,y}[t]=g \left(I_{x,y}[t]+R_{x,y}[t]+D_{x,y}(t)) \right)</math>, | ||
where | where | ||
| − | * <math>I_{x,y}[t]</math> is the number of photoelectrons | + | * <math>I_{x,y}[t]</math> is the number of photoelectrons generated during interval <math>t</math>, |
* <math>R_{x,y}[t]</math> is the read noise during time interval <math>t</math>, | * <math>R_{x,y}[t]</math> is the read noise during time interval <math>t</math>, | ||
* and <math>D_{x,y}[t]</math> is the number of dark current electrons generated during time interval <math>t</math> | * and <math>D_{x,y}[t]</math> is the number of dark current electrons generated during time interval <math>t</math> | ||
| − | The variance | + | 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 <math>\operatorname{Var}(P_{x,y})</math> can be found by summing the variances of the three individual terms. The photoelectron count, <math>I_{x,y}</math>, is Poisson distributed, so its variance is equal to its mean: <math>\operatorname{Var}(I_{x,y})=\langle I_{x,y} \rangle</math>. The second term has a constant variance that is a property of the camera, the read noise <math>N_r</math>. The third term is also Poisson distributed, with an average value of <math>I_d \delta t</math>, where <math>\delta t</math> is the exposure time. This gives: |
| − | + | ||
| − | <math>I_{x,y}</math> is Poisson distributed, so its variance is equal to its mean | + | |
:<math>\text{Var}\left(P_{x,y}\right)=g\left(\langle I_{x,y}\rangle+N_r^2 + i_d \delta t \right)</math> | :<math>\text{Var}\left(P_{x,y}\right)=g\left(\langle I_{x,y}\rangle+N_r^2 + i_d \delta t \right)</math> | ||
{{Template:20.309 bottom}} | {{Template:20.309 bottom}} | ||
Revision as of 22:32, 22 September 2015
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 I_{x,y} $, where $ P_{x,y} $ is the number of counts measured at pixel location $ x $, $ y $.
- 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) $
