# Will I be able to differentiate 1500 molecules from 1475? What's the dynamic range?

##### THIS GUIDE IS FOR:

Biologists that use, or are interested in using, microscope cameras and don’t speak engineering

##### THIS GUIDE OFFERS:

Clarity on the relevance of camera specs to biological experimentation

## LISTED IN SPECIFICATIONS AS:

Hamamatsu listing Synonyms used by other vendors
Full well capacity Pixel well depth
Full well capacity EM-CCD readout Shift register well depth, Gain register pixel well depth
Dynamic range
A/D conversion A/D conversion factor, Digitization, Digital output format

As with many scientific questions, the answer to the seemingly simple question, “Will I be able to differentiate 1500 molecules from 1475,” is not straightforward. It depends on the photon emission properties of the fluorophore, the number of fluorophores per molecule, and the camera. The heart of this question is understanding the detectable signal change that your camera is able to detect for your specific experiment. And to understand detectable signal change, we need to look at full well capacity.

Detectable signal change (DSC) describes sensitivity to change. For the case of a microscope camera, DSC describes the measureable precision of a change in the signal, making total signal acquired the limiting factor. Full well capacity—which defines the maximum amount of signal the camera can detect—is the most important feature and camera noise is of minimal importance.

Back to the question of detecting 1500 molecules versus 1475, the question becomes, “can I detect a 2 % difference?” Using the following equations for DSC and % DSC:

$DSC=\sqrt{\mathstrut S}$
$\%\ DSC=\sqrt{S/S}$

and solving for S:

$0.02=\sqrt{S/S}$
$0.02\ S\ =\sqrt{\mathstrut S}$
$0.0004\ S^{2} =S$
$S=1/0.0004=2500$

Our camera would need to be able to have enough full well capacity to capture 2500 electrons before saturating.

Of course, our sample would need to produce enough photons to create that many electrons in the detector in the time allotted by the exposure and the quantum efficiency of the system.

But what if you wanted to detect this 2 % difference while also keeping other features in the image visible (above noise) and non-saturating. For example, if you were trying to image neurons, where the cell bodies are bright, but the dendrites are much dimmer. Now you need to consider the dynamic range (DR) of the camera.

The total DR of the camera is also a function of the full well capacity, but here camera noise is important to consider. Note that DR does not consider the sample, it is only a property of the camera.

DR is defined as the maximum achievable signal divided by the camera noise.

$Dynamic\ range=S/N$

And is sometimes presented in decibels instead of as a ratio:

$Dynamic\ range\ in\ decibels(Db)=20\cdot log(S/N)$

The maximum achievable signal is determined by the full well capacity—if the full well capacity is 30,000 electrons, then the maximum number of photons you can collect in one image for that pixel is 30,000. Of course, because not every photon is converted into an electron, this reflects only a fraction of the actual number of photons and is described by the Quantum Efficiency (QE) of the camera at that particular wavelength.

And noise is a combination of read noise, dark noise, and shot noise (discussed in greater detail here). Typically, you can calculate dynamic range using the full well capacity and the read noise. For most biological experiments, dark noise is negligible and only affects the dynamic range at exposures longer than five minutes, and at high signal shot noise is also negligible.

$Total\ noise=\sqrt{\mathstrut read\ noise^2 + dark\ noise^2 +shot\ noise^2}$

Using the ORCA-Flash4.0 as an example, we divide the full well capacity of 30,000 electrons by the read noise at slow scan, which is 0.9 electrons, to get a dynamic range of 33,000: 1, or 90.4 Db.

Note that for EM-CCDs, when using the EM register dynamic range can be reduced. Once the full well capacity of the EM gain register exceeds the amplified full well capacity of the individual pixel, dynamic range decreases. The net result is a tradeoff between high EM gain and wide dynamic range.

### A word about bit depth

It’s important to recognize that bit depth and dynamic range are not synonymous. Full well capacity divided by bit depth establishes the limit of precision for each gray level—it gives the value for how many electrons per gray level (digitizer bit).

For quantitative image analysis and feature classification, high bit depth is essential.

## BOTTOM LINE:

• Dynamic range provides an indication of how many different intensity levels the camera can distinguish, but actual detectable signal change depends on the intensity of your samples and the camera.
• If the manufacturer does not list dynamic range, it can be calculated from the full well capacity and read noise.
• In EM-CCDs as EM gain is increased, dynamic range decreases.

NEXT SECTION: My samples have very low signal; can this camera accurately image my sample?