Cornelius DPC 230 Specifications Page 13
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Absolute-Timing Modes 7
The autocorrelation (shown left) has a sharp peak at
τ
= 0. (The function correlates perfectly
with itself). The slow fluctuations in I(t) represent themselves in a high correlation at medium
τ
. For
τ
longer than the typical time of the slow fluctuations G(
τ
) drops to very low values.
The cross-correlation function of the two signals, I1 and I2, is shown right. The slow fluctua-
tions in I
1
and I
2
have the same general appearance. However, the noise in I
1
and I
2
is differ-
ent. Therefore only the fluctuations correlate and give a noticeable contribution to G
12
(
τ
).
The equations shown above are appropriate to calculate correlation functions from analog
signals. The do, however, not well apply to time-tagged photon counting data recorded at high
time resolution. Such data do not display a continuous waveform as shown in Fig. 9 but are
rather a random sequence of individual detection events.
The general correlation procedure for time-tagged photon data is demonstrated in Fig. 10. In
typical TDC data, the time-channel width, T, is shorter than the dead time of the detec-
tor/photon counter combination. Therefore only one photon can be recorded in a particular
time channel. Consequently, N(t) and N(t +
τ
) can only be 0 or 1. The calculation of the auto-
correlation function therefore becomes a simple shift, compare, and histogramming procedure.
The times of the individual photons are subsequently shifted by one time-channel interval, T,
and compared with the original detection times. The coincidences found between the shifted
and the unshifted data are transferred into a histogram of the number of coincidences, G, ver-
sus the shift time,
τ
. The obtained G(
τ
) is the (un-normalised) autocorrelation function.
t
t
t
t
Number of coincidences
Photon times
2T
3T
=T
G
=
=
Fig. 10: Calculation of the autocorrelation function from TCSPC time-tag data
The cross-correlation function between two signals is obtained by a similar procedure. How-
ever, the photon times of one detector channel are shifted versus the photon times of another
channel.
The result of the shift-and-compare procedure is not normalised. Normalisation can be inter-
preted as the ratio of the number of coincidences found in the recorded signal to the number of
coincidences expected for an uncorrelated signal of the same count rate. The normalised auto-
correlation and cross-correlation functions are
2
)()(
P
T
n
N
n
GG
ττ
=
with n
T
= total number of time intervals, Np = total number of photons, and
21
1212
)()(
PP
t
n
NN
n
GG
ττ
=
with n
T
= total number of time intervals, N
p1
= total number of photons in signal 1, N
p2
= total
number of photons in signal 2.
- 16 Channel 1
- Photon Correlator 1
- User Handbook 1
- (c) Becker & Hickl GmbH 2
- DPC-230 3
- 16 Channel Photon Correlator 3
- II 4
- Contents 5
- IV 6
- Introduction 7
- DPC-230 Architecture 8
- Relative Timing 9
- Operation Modes 11
- Fluorescence Correlation 12
- Absolute-Timing Modes 7 13
- Relative Timing Modes 14
- TCSPC Mode 15
- TCSPC with Absolute Timing 16
- Imaging 17
- 12 Operation Modes 18
- Installation 19
- Hardware Installation 20
- Driver Installation 20
- Software Start 21
- 22
- Operating the DPC-230 23
- CFD Inputs 24
- CFD Inputs 19 25
- Typical Applications 27
- 22 Typical Applications 28
- 26 Typical Applications 32
- 28 Typical Applications 34
- Anti-Bunching 35
- 30 Typical Applications 36
- Ti:Sa or ps diode 37
- 32 Typical Applications 38
- 34 Typical Applications 40
- 36 Typical Applications 42
- SPCM Software 43
- Display and Trace Parameters 44
- Link to Data Analysis 46
- Trace Statistics 47
- Status Information 47
- 42 SPCM Software 48
- Operation Mode 49
- 44 SPCM Software 50
- Name of Time-Tag Data File 51
- Configuring the Inputs 52
- CFD and SYNC Parameters 53
- SYNC Frequency Divider 53
- TDC Parameters 54
- Fig. 81: Save panel 55
- Fig. 82: Save options 56
- Fig. 83: Load panel 56
- Predefined Setups 57
- 52 SPCM Software 58
- Importing FIFO Files 59
- 56 SPCM Software 62
- Specification 65
- References 67
- 62 References 68
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