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        <dc:date>2017-09-26T11:46:03+00:00</dc:date>
        <dc:creator>Anonymous (anonymous@undisclosed.example.com)</dc:creator>
        <title>differential_count_rate</title>
        <link>https://www.tcspc.de/doku.php/glossary:differential_count_rate?rev=1506426363&amp;do=diff</link>
        <description>&lt;table&gt;&lt;tr&gt;&lt;th colspan=&quot;2&quot; width=&quot;50%&quot;&gt;2017/09/24 05:34&lt;/th&gt;&lt;th colspan=&quot;2&quot; width=&quot;50%&quot;&gt;current&lt;/th&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class=&quot;diff-blockheader&quot; colspan=&quot;2&quot;&gt;Line 17:&lt;/td&gt;
&lt;td class=&quot;diff-blockheader&quot; colspan=&quot;2&quot;&gt;Line 17:&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;Not really. In case of pulsed signals the average count rate is a misleading quantity. An average count rate value does not take into account **when** and **how** those photons are emitted and detected. Interpreting a 100 kcps intensity as a constant emission rate (Poisson mean rate, in math terms) is a misconception. The physics of the measurement is completely different. These photons are obviously not emitted evenly, one by one over the whole one second period. They arrive to the detector bunched, as flashes. These are short time intervals with huge photon density (rate), separated by long &amp;quot;dark&amp;quot;, quiet periods.&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;Not really. In case of pulsed signals the average count rate is a misleading quantity. An average count rate value does not take into account **when** and **how** those photons are emitted and detected. Interpreting a 100 kcps intensity as a constant emission rate (Poisson mean rate, in math terms) is a misconception. The physics of the measurement is completely different. These photons are obviously not emitted evenly, one by one over the whole one second period. They arrive to the detector bunched, as flashes. These are short time intervals with huge photon density (rate), separated by long &amp;quot;dark&amp;quot;, quiet periods.&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;-&lt;/td&gt;&lt;td class=&quot;diff-deletedline&quot;&gt;&lt;strong class=&quot;diff-mark&quot;&gt;Getting&amp;#160;&lt;/strong&gt;a final count at &amp;quot;1% of SYNC rate&amp;quot; is a result of **&lt;strong class=&quot;diff-mark&quot;&gt;low&amp;#160;&lt;/strong&gt;sampling&amp;#160;&lt;strong class=&quot;diff-mark&quot;&gt;rate&lt;/strong&gt;**&amp;#160;&lt;strong class=&quot;diff-mark&quot;&gt;of&amp;#160;&lt;/strong&gt;a&amp;#160;&lt;strong class=&quot;diff-mark&quot;&gt;high rate signal&lt;/strong&gt;.&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;+&lt;/td&gt;&lt;td class=&quot;diff-addedline&quot;&gt;&lt;strong class=&quot;diff-mark&quot;&gt;In yet another words, achieving&amp;#160;&lt;/strong&gt;a final count&amp;#160;&lt;strong class=&quot;diff-mark&quot;&gt;rate&amp;#160;&lt;/strong&gt;at &amp;quot;1% of SYNC rate&amp;quot; is a result of **&lt;strong class=&quot;diff-mark&quot;&gt;sparse&amp;#160;&lt;/strong&gt;sampling&amp;#160;&lt;strong class=&quot;diff-mark&quot;&gt;with dead time&lt;/strong&gt;**&lt;strong class=&quot;diff-mark&quot;&gt;. The sampled signal features much higher photon density, but lasts only for&amp;#160;&lt;/strong&gt;a&amp;#160;&lt;strong class=&quot;diff-mark&quot;&gt;short time&lt;/strong&gt;.&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;In mathematical terms, &amp;quot;average count rate of 1..2% of SYNC rate&amp;quot; means the overall detection probability, integrated over the whole duration of a measurement. The concept of //differential count rate// is related to the //probability density function//. The detected signal in TCSPC has a very inhomogeneous time distribution.&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;In mathematical terms, &amp;quot;average count rate of 1..2% of SYNC rate&amp;quot; means the overall detection probability, integrated over the whole duration of a measurement. The concept of //differential count rate// is related to the //probability density function//. The detected signal in TCSPC has a very inhomogeneous time distribution.&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;Note: for detectors that exhibit count rate dependent shifting of the IRF, extra care has to be taken when measuring the IRF and directly using it for decay analysis. ((Takuhiro Otosu, Kunihiko Ishii and Tahei Tahara, Note: Simple calibration of the counting-rate dependence of the timing shift of single photon avalanche diodes by photon interval analysis, Rev. Sci. Instrum. **84**, 036105 (2013); [[http://dx.doi.org/10.1063/1.4794769]]))&lt;/td&gt;&lt;td class=&quot;diff-lineheader&quot;&gt;&amp;#160;&lt;/td&gt;&lt;td class=&quot;diff-context&quot;&gt;Note: for detectors that exhibit count rate dependent shifting of the IRF, extra care has to be taken when measuring the IRF and directly using it for decay analysis. ((Takuhiro Otosu, Kunihiko Ishii and Tahei Tahara, Note: Simple calibration of the counting-rate dependence of the timing shift of single photon avalanche diodes by photon interval analysis, Rev. Sci. Instrum. **84**, 036105 (2013); [[http://dx.doi.org/10.1063/1.4794769]]))&lt;/td&gt;&lt;/tr&gt;
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