Hybrid Photodiode - Revision history

Senderovich: /* Results */

2008-07-28T17:38:19Z

Results

Senderovich: /* Modeling the HPD spectrum */

2008-07-28T17:37:17Z

Modeling the HPD spectrum

Senderovich at 17:33, 28 July 2008

2008-07-28T17:33:24Z

Senderovich at 17:23, 28 July 2008

2008-07-28T17:23:35Z

Senderovich at 17:22, 28 July 2008

2008-07-28T17:22:35Z

Senderovich at 17:20, 28 July 2008

2008-07-28T17:20:21Z

Senderovich: /* Results */

2008-07-28T17:18:42Z

Results

Senderovich at 16:52, 28 July 2008

2008-07-28T16:52:32Z

Senderovich at 19:46, 16 July 2008

2008-07-16T19:46:27Z

Senderovich: /* Results */

2008-07-16T19:26:33Z

Results

← Older revision		Revision as of 17:38, 28 July 2008
Line 113:		Line 113:
	[[Image:HPD_3dist.png\|frame\|Distributions on a logarithmic plot from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]		[[Image:HPD_3dist.png\|frame\|Distributions on a logarithmic plot from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]

−	Fits with far better agreement were found when the above-listed parameters were free to vary individually for each distribution. Similar and more drastic problems occurred when the simpler on-Gaussian model was used for the distribution of secondary photo-electrons. Evidently, the inaccuracy in its shape is compounded with more convolutions ~~present~~ in the high-photon count ~~spectrum~~. Thus, we suspect that the two-Gaussian approximation of this asymmetric distribution is yet not full adequate. However, this already computationally-intensive model (note the three summations) will be even more difficult with more Gaussian and intractable for an arbitrary shape since the convolutions will no longer be straightforward. Disagreements between the fit and data in the right-hand tails of the spectra may also be due to the truncation of the summation in ''n'' corresponding to the number of peaks present due to the convolution with primary and secondary distributions.	+	Fits with far better agreement were found when the above-listed parameters were free to vary individually for each distribution. Similar and more drastic problems occurred when the simpler one-Gaussian model was used for the distribution of secondary photo-electrons. Evidently, the inaccuracy in its shape is compounded with more convolutions necessary in the high-photon count spectra. Thus, we suspect that the two-Gaussian approximation of this asymmetric distribution is yet not full adequate. However, this already computationally-intensive model (note the three summations) will be even more difficult with more Gaussian and intractable for an arbitrary shape since the convolutions will no longer be straightforward. Disagreements between the fit and data in the right-hand tails of the spectra may also be due to the truncation of the summation in ''n'' corresponding to the number of peaks present due to the convolution with primary and secondary distributions.

← Older revision		Revision as of 17:37, 28 July 2008
Line 113:		Line 113:
	[[Image:HPD_3dist.png\|frame\|Distributions on a logarithmic plot from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]		[[Image:HPD_3dist.png\|frame\|Distributions on a logarithmic plot from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]

−	~~Far~~ better agreement ~~fits~~ were found when the above-listed parameters were free to vary individually for each distribution. Similar and more drastic problems occurred when the simpler on-Gaussian model was used for the distribution of secondary photo-electrons. Thus, we suspect that the two-Gaussian approximation of this asymmetric distribution is not full adequate. However, this already computationally-intensive model (note the three summations) will be even more difficult with more Gaussian and intractable for an arbitrary shape since the convolutions will no longer be straightforward. Disagreements between the fit and data in the right-hand tails of the spectra may also be due to the truncation of the summation in ''n'' corresponding to the number of peaks present due to the convolution with primary and secondary distributions.	+	Fits with far better agreement were found when the above-listed parameters were free to vary individually for each distribution. Similar and more drastic problems occurred when the simpler on-Gaussian model was used for the distribution of secondary photo-electrons. Evidently, the inaccuracy in its shape is compounded with more convolutions present in the high-photon count spectrum. Thus, we suspect that the two-Gaussian approximation of this asymmetric distribution is yet not full adequate. However, this already computationally-intensive model (note the three summations) will be even more difficult with more Gaussian and intractable for an arbitrary shape since the convolutions will no longer be straightforward. Disagreements between the fit and data in the right-hand tails of the spectra may also be due to the truncation of the summation in ''n'' corresponding to the number of peaks present due to the convolution with primary and secondary distributions.

← Older revision		Revision as of 17:33, 28 July 2008
Line 111:		Line 111:
	\|}		\|}

−	[[Image:HPD_3dist.png\|Distributions from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]	+	[[Image:HPD_3dist.png\|frame\|Distributions on a logarithmic plot from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]
		+
		+	Far better agreement fits were found when the above-listed parameters were free to vary individually for each distribution. Similar and more drastic problems occurred when the simpler on-Gaussian model was used for the distribution of secondary photo-electrons. Thus, we suspect that the two-Gaussian approximation of this asymmetric distribution is not full adequate. However, this already computationally-intensive model (note the three summations) will be even more difficult with more Gaussian and intractable for an arbitrary shape since the convolutions will no longer be straightforward. Disagreements between the fit and data in the right-hand tails of the spectra may also be due to the truncation of the summation in ''n'' corresponding to the number of peaks present due to the convolution with primary and secondary distributions.

@@ Line 73: / Line 73: @@
 \left( \begin{matrix} n\\k \end{matrix} \right)
 (1-\alpha-\beta)^{m-n} \alpha^{n-k} \beta^{k}
-\ G\left( (m-n) + (n-k)p + kr,\ (m-n)\sigma_1^2 + (n-k)\sigma_2^2 + k\sigma_3^2 \right)
+\ G\left( (m-n) + (n-k)p + kr,\ \sigma_0^2 + (m-n)\sigma_1^2 + (n-k)\sigma_2^2 + k\sigma_3^2 \right)
 </math>
@@ Line 107: / Line 107: @@
 ||
 Widths of primary peaks and overall noise:
-* ''&sigma;''<sub>0</sub> || 13.7  p.e.
+* ''&sigma;''<sub>0</sub> = 13.7&nbsp;p.e.
-* ''&sigma;''<sub>1</sub> || 0.881 p.e.
+* ''&sigma;''<sub>1</sub> = 0.881&nbsp;p.e.
 |}
 [[Image:HPD_3dist.png|Distributions from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]

@@ Line 92: / Line 92: @@
 {| border="0" cellpadding="20"
+|
 {| style="text-align:center" border="1" cellspacing="0" cellpadding="5"
 |- style="background:#F1F2FF"
@@ Line 111: / Line 105: @@
 |-
 |}
 |}
 [[Image:HPD_3dist.png|Distributions from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]

@@ Line 88: / Line 88: @@
 The parameters relating to the shape of the primary and secondary electron distributions, as well as an additional Gaussian noise factor (''&sigma;''<sub>0</sub>) were allowed to vary. A fit with these degrees of freedom was performed on three distributions from drastically different light levels (corresponding to roughly 64, 530 and 973 primary detected photons.) The following model parameters produced reasonably good fits (''&chi;''<sup>2</sup>&lt;2.0) for all three distributions.
@@ Line 114: / Line 112: @@
 |}
 |}

← Older revision		Revision as of 17:18, 28 July 2008
Line 87:		Line 87:
	* Pedestal position: -3.6606 × 10<sup>-3</sup> V;		* Pedestal position: -3.6606 × 10<sup>-3</sup> V;

−	The parameters relating to the shape of the primary and secondary electron distributions, as well as an additional Gaussian noise factor were allowed to vary. A fit with these degrees of freedom was performed on three distributions from drastically different light levels (corresponding to roughly 64, 530 and 973 primary detected photons.) The following model parameters produced reasonably good fits (''χ''<sup>2</sup><2.0) for all three distributions.	+	The parameters relating to the shape of the primary and secondary electron distributions, as well as an additional Gaussian noise factor (''σ''<sub>0</sub>) were allowed to vary. A fit with these degrees of freedom was performed on three distributions from drastically different light levels (corresponding to roughly 64, 530 and 973 primary detected photons.) The following model parameters produced reasonably good fits (''χ''<sup>2</sup><2.0) for all three distributions.
		+
		+	[[Image:HPD_3dist.png\|Distributions from runs with different light levels (roughly 64, 530 and 973 primary detected photons.) Units are arbitrary and histograms have been rescaled for comparison.]]

@@ Line 87: / Line 87: @@
 * Pedestal position: -3.6606&nbsp;&times;&nbsp;10<sup>-3</sup>&nbsp;V;
-The parameters relating to the shape of the primary and secondary electron distributions, as well as an additional Gaussian noise factor were allowed to vary.
+The parameters relating to the shape of the primary and secondary electron distributions, as well as an additional Gaussian noise factor were allowed to vary. A fit with these degrees of freedom was performed on three distributions from drastically different light levels (corresponding to roughly 64, 530 and 973 primary detected photons.) The following model parameters produced reasonably good fits (''&chi;''<sup>2</sup>&lt;2.0) for all three distributions.
@@ Line 93: / Line 93: @@
+|
 {|  style="text-align:center" border="1" cellspacing="0" cellpadding="5"
-| &sigma;<sub>0</sub> || 13.9  p.e.
+| ''&sigma;''<sub>0</sub> || 13.7  p.e.
 |-
-| &sigma;<sub>1</sub> || 0.857 p.e.
+| ''&sigma;''<sub>1</sub> || 0.881 p.e.
 |}
 ||
@@ Line 104: / Line 104: @@
 ! Units
 |-
-| p                   || 107.3   || r      || 115.2  || p.e.
+| ''p''                   || 107.0   || ''r''      || 179.5  || p.e.
 |-
-| &alpha;             || .000815 || &beta; ||.000524  || -
+| ''&alpha;''             || .000899 || ''&beta;'' ||.000299  || -
 |-
-| &sigma;<sub>2</sub> || 35.01   || &sigma;<sub>3</sub> || 132.9 || p.e.
+| ''&sigma;''<sub>2</sub> || 35.83   || ''&sigma;''<sub>3</sub> || 119.2 || p.e.
 |-
 |}
 |}

← Older revision		Revision as of 19:26, 16 July 2008
Line 82:		Line 82:

	[[Image:HPD_OnePEdist.png\|thumb\|300px\|Distributions of primary and secondary photoelectron signals (noise included) for one incident primary photoelectron.]]		[[Image:HPD_OnePEdist.png\|thumb\|300px\|Distributions of primary and secondary photoelectron signals (noise included) for one incident primary photoelectron.]]
		+
		+
		+	Fixed parameters from HPD specifications and no-light distribution ("pedestal") measurement:
		+	* Total gain, including amplifier and oscilloscope waveform mean rescaling: 1.9264 × 10<sup>5</sup> V/p.e.;
		+	* Pedestal position: -3.6606 × 10<sup>-3</sup> V;
		+
		+	{\| style="text-align:center" border="1" cellspacing="0" cellpadding="5"
		+	\|-
		+	! colspan="2"\| Gaussian 1
		+	! colspan="2"\| Gaussian 2
		+	\|-
		+	\| p \|\| 107.3 \|\| r \|\| 115.2
		+	\|-
		+	\| α \|\| .000815 \|\| β \|\|.000524
		+	\|-
		+	\| σ<sub>2</sub> \|\| 35.01 \|\| σ<sub>3</sub> \|\| 132.9
		+	\|-
		+	\|}