Microscopy Cheat-Sheet

Scale Factor

Probably the most important piece of metadata and the one that is usually needed first, is the scale factor. The scale factor tells us what area a pixel represents on our specimen.

 scale-factor-formula-1

scale-factor-formula-2

d : dimension of a single pixel on the CCD/CMOS chip μm
b : binning (camera setting to aggregate several neighboring pixel) m: objective magnification
c : camera mount magnification
M: total magnification between sample and the camera

Note that for laser scanning confocal microscopes this formula does not apply as is, since the scanner of the instrument allows for arbitrary sampling areas (within the scanners capabilities) and the sampling density can vary. The easiest is to use the original files produced by the instrument (do not export tif, png or jpg) and to get the pixel size from the metadata. With ImageJ (Fiji), you can open most of the microscope formats using Menu > Plugins > Bio-Formats > Bio-Formats Importer. Usually the scale factor is already set correctly (check Menu > Analyze > Set Scale).

Sampling

To do accurate measurements, it is essential to properly configure the instruments. If the sampling for a given experiment is not correct, there is little that can be done to salvage the measurement during the image processing.

The following paragraphs give an overview for the most important parameter, to consider while setting up an acquisition with a microscope.

Intensity

The goal here is to spread the signal from our objects of interest over the entire dynamic range of our detector.  To this end we want pixels considered background close to zero and the brightest object pixel just bellow the maximum value. Pixels we use later for measurements should not be underexposes nor saturated, in order to know the true value.

On the other hand, anything not considered an object of interest, e.g. specs of dust, can be outside of the detector range.

intensity sampling

Three cases to configure the detector. The first mode represents mostly background, the second mode on the right, represents the object in a fluorescent image.
Left: the dynamic range of the detector is not fully used, come pixels are underexposed. Middle: optimal configuration with no saturation and the object pixels spread over the dynamic range of the detector -> good contrast. Right: configuration leading to saturation, a third mode (single bin) on the far right of the histogram appears.

 

Spacial

The Nyquist criterion, coming initially from signal processing (determined for 1D signals), serves as a guideline to determine the optimal pixel size (physical distance one pixel represents on the specimen).
A detailed explanation can be found on the SVI-wiki.

Nyquist criterion:

nyquist criterion

nyquist-2f-phase-example

Exampling of how a different phase can cause artifacts when the Nyquist criterion is not respected.

 

On the other hand objectives only can resolve so much detail. Having a pixel size far bellow the Rayleigh criterion for a given objective is also called over sampling. This means that despite having a very small pixel size, the objective will not be able to resolve additional information. Therefore oversampling usually results in creating redundant information, that does not achieve anything but to increase the data volume without additional information.

Abbe’s lateral resolution formula (x-y-resolution):

abbe_xy-res

Abbe’s axial resolution formula (z-resolution)

abbe_z-res

Rayleigh criterion:

rayleigh-criterion

 

NA: numerical aperture
λ: wavelength
Θ: half of the objective angular aperture
Θmax: ∼144◦
1.22 : Constant derived from Bessel functions
R : smallest resolved distance

 

Temporal

When acquiring movies, there are two essential parameters, that will determine the accuracy of your measurements over time:

  • frame rate (movie speed)
  • observation time (duration of the movie)

To determine these parameter, it is a good strategy to acquire a movie at a high speed and over a long duration. Then by subsampling the video for frame rates and observation times, we can repeat the measurements and plot them against the frame rate/observation time.

For the frame rate, we usually will find this way a point where the measurement will start to fluctuate. Hence we need to choose a frame rate smaller than the one where we start to observe fluctuations.

Plot of the measurements to determine optimal frame rate. The shoulder of the curve indicates the critical value ~0.1, above which the measurement starts to fluctuate.

For the observation time we can similarly observe a point where the variation of the measurement decreases. Once the variations of the measurements will converge on the standard measurement fluctuations we reached the point where the observation time is long enough to quantify the desired phenomenon.

Plot of the measurements to determine the minimum observation time. The value of ~15 sec. is the critical value, above which the variations start to be constant for a given measurement, consequently the observation time should not be chosen bellow this value.

 

Optimizing sampling parameter

In an ideal world, we would choose the optimal parameters of intensity, spacial and temporal sampling. But due to technical limitations (detector sensitivity, maximum frame rate, etc.) we often need to find the optimal compromise between feasibility and best possible sampling.

Bellow we have the trade-off circle of parameters. We also should keep an eye on the data volume produced during the acquisition.

The trade-off circle. Blue; acquisition parameter. Gray; microscope parameter that impact the acquisition. The plus sign indicates parameter that can improve an acquisition parameter and the minus sign indicates parameter that can have a diminishing effect.