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Dynamic Range & EMCCDs

Uncovering the Facts

Calculating dynamic range in EMCCDs has often been a source of confusion, due to the
additional requirement to factor in EM gain and the extended well capacity of the gain
register. High dynamic range can be accessed in EMCCDs with careful fine tuning
of EM gain.

**Dynamic Range (DR) is given by: **

DR = Full well capacity + Detection limit

Calculating Dynamic Range in an EMCCD camera is a slightly more
complicated story than for conventional CCDs. This is because of the
favourable effect of EM gain on the detection limit vs. the limiting
effect of EM gain on the full well capacity. The easiest way to address
this is to first take each parameter separately:

**Detection Limit and EM gain**

The main function of EMCCD is to eliminate the read noise detection
limit and enable detection of weak photon signals that would otherwise
be lost within this noise floor. With EM gain, the detection limit is
given by the 'Effective Read Noise', i.e. the read noise divided by the
gain multiplication, down to one electron. Why never less than one?
This stems from the definition of detection limit, which is essentially
"the signal equal to the lowest noise level". Since you can't get a
signal less than one photon, then the detection limit should never be
taken as less than one electron.

For example, the iXon Ultra 888 has a read noise of ~45 electrons @10
MHz with EM gain off. At EM gain x2, the new detection limit can
be considered to be 22.5 electrons effective read noise, at x5 it will
be 9 electrons, at x45 it will be 1 electron. At x100, the Effective
Read Noise will be 0.45 electrons, but as far as the dynamic range calculation is
concerned, this detection limit must still be treated as 1 electron.

**Full Well Capacity and EM gain**

One might imagine that applying EM gain will decrease the full well
pixel capacity proportionally. This is indeed the case, but a buffer has
been built into EMCCD cameras to enable at least some EM gain to
be applied while maintaining the original well capacity. This buffer
is in the form of a higher capacity in the gain register pixels, where
the multiplication actually takes place. So, the true capacity is given
by the capacity of the pixels of the sensor, but as you apply EM gain
this holds only up until the point where the larger capacity of the gain
register pixels also become saturated by applied EM gain. After that
point, you have to correct the 'effective' full well of the sensor to be
equal to the full well of the gain register divided by the gain.

**Dynamic Range and EM gain**

These above factors combined mean that as EM gain is increased,
Dynamic Range will increase with gain to a maximum, level off and
then reach a point at which it begins to deplete again with further gain.

iXon Ultra 888 back-illuminated EMCCD can be read out at either
30, 20, 10 or 1 MHz speeds. This offers extended flexibility
to balance Dynamic Range vs. frame rates. Furthermore
OptAcquire can be used to select optimal Dynamic Range
settings at fastest and slowest speeds.

This can seem complicated, but fortunately these DR vs EM gain
relationships can be readily plotted out and visualized in graphical
form, as exemplified in Figure 1.

There are a number of interesting points to note from these plots:

- The rationale behind offering readout speeds slower than 17
MHz through the EM-amplifier is so that frame rate can be traded off
against dynamic range. You can see that the highest dynamic range
through an EM amplifier comes from the slowest 1 MHz readout
speed.
- At any readout speed through the EM-amplifier, the best
combination of Dynamic Range and sensitivity can be obtained at an
EM gain setting equal to the readout noise at that speed. At this point
the DR is at maximum and the effective readout noise is 1 electron
(i.e. just on the verge of single photon sensitivity).
- At x1000 EM gain the dynamic range is only 400:1. Excessively
high EM gain can also accelerate EM gain ageing in back-illuminated
EMCCDs (see section 7). EM gains of x300 or less are more than
sufficient to optimize sensitivity, while ensuring dynamic range
is not excessively compromised. The only occasions when Andor
recommends extending EM gain to x1000 is for single photon
counting experiments.
- The highest dynamic range is through the conventional CCD
amplifier.
- It is clear that the actual sensor Dynamic Range only exceeds
14-bits at 1 MHz, through either EM or a conventional amplifier.
Therefore, it is at 1 MHz that it becomes important to match this
higher dynamic range output with a scientific grade, noise free 16-bit
A/D digitization.

**Note: There is a direct relationship between readout noise and
maximum dynamic range at a given readout speed. Lower
readout noise affords higher dynamic range. The readout noise
specification used in calculating dynamic range must be with
EM gain turned off, as quoted in all iXon spec sheets. We note,
however, that another prominent EMCCD provider chooses to
quote their lowest read noise value, not for EM gain-off, but only
for EM gain x4, x6 or x10 (model dependent). In this case, to
arrive at the real read noise spec you would have to multiply the
quoted figure by x4, x6 or x10.**