Difference between revisions of "Shot noise and centroid finding"
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[[Image:Simulated Shot Noise.png|Simulated image of a fluorescent microshpere at various signal to noise ratios.]] | [[Image:Simulated Shot Noise.png|Simulated image of a fluorescent microshpere at various signal to noise ratios.]] | ||
| − | Shot noise is a fluctuation that affects all light intensity measurements, including microscopic images recorded with a CCD camera. <ref>There are a few exotic methods, such as | + | Shot noise is a fluctuation that affects all light intensity measurements, including microscopic images recorded with a CCD camera. <ref>There are a few exotic methods, such as <a href="http://www.rp-photonics.com/amplitude_squeezed_light.html">"amplitude-squeezed light" </a> that reduce noise below the shot noise level.</ref> It is a consequence the discrete and the stochastic nature of photon emission. Poisson statistics provide an excellent model for shot noise. The standard deviation of a Poisson-distributed random variable is equal to the square root of its average value. Thus, the lowest possible signal to noise ratio of an intensity measurement is equal to the square root of the average number of photons (intensity). The simulated images above show the effect of shot noise on the image of a fluorescent microsphere with a radius of 10 pixels for several values of intensity. |
One method to estimate the position of a microsphere in an image is to compute an intensity-weighted centroid (also called the center of mass). Intensity-weighted centroids can provide locations accurate to a fraction of a pixel. Shot noise causes random variation in the pixel intensities, which perturbs the centroid. Thus, repeated localizations of a stationary particle will exhibit random variation. Deriving an analytical expression for the variation is tedious. Happily, patient people with exceptional mathematical abilities have taken the time to do so. (See, for example, this reference: <a href="http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-27-9-2038">Hui Jia, Jiankun Yang, and Xiujian Li. Minimum variance unbiased subpixel centroid estimation of point image limited by photon shot noise.</a>). The variation in the centroid is approximately proportional to the square root of intensity, also. | One method to estimate the position of a microsphere in an image is to compute an intensity-weighted centroid (also called the center of mass). Intensity-weighted centroids can provide locations accurate to a fraction of a pixel. Shot noise causes random variation in the pixel intensities, which perturbs the centroid. Thus, repeated localizations of a stationary particle will exhibit random variation. Deriving an analytical expression for the variation is tedious. Happily, patient people with exceptional mathematical abilities have taken the time to do so. (See, for example, this reference: <a href="http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-27-9-2038">Hui Jia, Jiankun Yang, and Xiujian Li. Minimum variance unbiased subpixel centroid estimation of point image limited by photon shot noise.</a>). The variation in the centroid is approximately proportional to the square root of intensity, also. | ||
As a result, the measured diffusion coefficient of a completely stationary particle will not be zero, and the measured diffusion coefficient of a non stationary particle will be systematically increased. | As a result, the measured diffusion coefficient of a completely stationary particle will not be zero, and the measured diffusion coefficient of a non stationary particle will be systematically increased. | ||
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Revision as of 21:58, 9 October 2012
Shot noise is a fluctuation that affects all light intensity measurements, including microscopic images recorded with a CCD camera. [1] It is a consequence the discrete and the stochastic nature of photon emission. Poisson statistics provide an excellent model for shot noise. The standard deviation of a Poisson-distributed random variable is equal to the square root of its average value. Thus, the lowest possible signal to noise ratio of an intensity measurement is equal to the square root of the average number of photons (intensity). The simulated images above show the effect of shot noise on the image of a fluorescent microsphere with a radius of 10 pixels for several values of intensity.
One method to estimate the position of a microsphere in an image is to compute an intensity-weighted centroid (also called the center of mass). Intensity-weighted centroids can provide locations accurate to a fraction of a pixel. Shot noise causes random variation in the pixel intensities, which perturbs the centroid. Thus, repeated localizations of a stationary particle will exhibit random variation. Deriving an analytical expression for the variation is tedious. Happily, patient people with exceptional mathematical abilities have taken the time to do so. (See, for example, this reference: <a href="http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-27-9-2038">Hui Jia, Jiankun Yang, and Xiujian Li. Minimum variance unbiased subpixel centroid estimation of point image limited by photon shot noise.</a>). The variation in the centroid is approximately proportional to the square root of intensity, also.
As a result, the measured diffusion coefficient of a completely stationary particle will not be zero, and the measured diffusion coefficient of a non stationary particle will be systematically increased.
- ↑ There are a few exotic methods, such as <a href="http://www.rp-photonics.com/amplitude_squeezed_light.html">"amplitude-squeezed light" </a> that reduce noise below the shot noise level.
