In the previous blog the focus was on binning (charge, voltage and digital domain) in the case the readout noise was dominating over the photon-shot noise.\u00a0 In other words, for the case of small signals or low light levels.\u00a0 This time, the situation for a shot-noise limited condition is considered.\u00a0 And actually the story can be very short : it does not matter when or where the binning is done, in all cases the result is exactly the same.<\/p>\n
For the charge domain<\/span> : if n x n<\/em> charge packets are added together, each with m<\/em> electrons, then after binning the final charge packet holds :<\/p>\n n x n x m<\/em> electrons.<\/p>\n The photon-shot noise in each individual charge packet was<\/p>\n sqrt(m)<\/em> electrons,<\/p>\n so the SNR for every individual charge packet was<\/p>\n SNR = m\/sqrt(m) = sqrt(m)<\/em>.<\/p>\n After binning the total photon-shot noise is equal to<\/p>\n sqrt(n x n x m)<\/em> electrons<\/p>\n and the SNR will be equal to :<\/p>\n SNR = n x n x m\/sqrt(n x n x m) = sqrt (n x n x m)<\/em>.<\/p>\n After binning in the charge domain, the increase in SNR will be<\/p>\n sqrt(n x n x m)\/sqrt(m) = n !<\/em><\/p>\n For the voltage domain<\/span> or digital domain<\/span> : if n x n<\/em> signals are added together, each with m<\/em> electrons, then before binning the output signal would have been k x m<\/em> V or DN, with k<\/em> being the conversion gain from input (charge) to output (Volts or Digital Numbers).\u00a0 Then after binning the final signal will be<\/p>\n n x n x k x m<\/em> V or DN.<\/p>\n The photon-shot noise of each individual signal before binning was<\/p>\n k x<\/em> sqrt(m)<\/em> V or DN,<\/p>\n so the SNR for the individual signal before binning was<\/p>\n SNR = (k x m)\/(k x sqrt(m)) = sqrt(m)<\/em>.<\/p>\n After binning the total photon-shot noise is equal to<\/p>\n k x sqrt(n x n x m)<\/em><\/p>\n and the SNR will be equal to :<\/p>\n SNR = (n x n x k x m)\/(k x sqrt(n x n x m)) = sqrt (n x n x m)<\/em>.<\/p>\n After binning in the voltage of digital domain, the increase in SNR will be<\/p>\n sqrt(n x n x m)\/sqrt(m) = n !<\/em><\/p>\n Conclusion : if there is enough light so that the performance of the sensor or the camera is shot-noise limited, it does not matter how the binning is realized, charge domain, voltage domain or digital domain.\u00a0 The increase of the SNR after binning is always equal to a factor n<\/em>, being the kernel size in the case of n x n<\/em> binned pixels.<\/p>\n Albert, 31-05-2016.<\/p>\n","protected":false},"excerpt":{"rendered":" In the previous blog the focus was on binning (charge, voltage and digital domain) in the case the readout noise was dominating over the photon-shot noise.\u00a0 In other words, for the case of small signals or low light levels.\u00a0 This time, the situation for a shot-noise limited condition is considered.\u00a0 And actually the story can […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1566","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1566","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1566"}],"version-history":[{"count":1,"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1566\/revisions"}],"predecessor-version":[{"id":1567,"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/1566\/revisions\/1567"}],"wp:attachment":[{"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1566"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1566"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/harvestimaging.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1566"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}