[an error occurred while processing this directive]
[an error occurred while processing this directive]
[an error occurred while processing this directive]
|
|
 |
|
|
| |
 |
|
A Practical Guide To 3D Sampling
by M. Messerli
This articles describes the practical implications of the Nyquist theorem on image acquisition in microscopy. Interested readers are referred to the literature (to be supplied here) for a discussion on the theory. The optimal sampling intervals (i.e. size of one pixel in x/y, step size along the optical axis) depend on the resolution of the objective lens. This in turn is depending on its numerical aperture only. Once a certain lens has been chosen the optimal sampling size is fixed and can easily be derived from the optical set-up. Please note: The information below applies only to fluorescence microscopy.
Sampling Intervall
As a rule of thumb the sample size (step size) should be half the resolution. We start the path of calculation with the calculation of the resolution which can be done as follows (fluorescence case)
alpha = ARCSIN(NA/RI)
dx = lambda / (4 * RI * SIN(alpha))
dz = lambda / (2 * RI * (1- COS(alpha)))
where
| alpha |
= |
aperture |
| RI |
= |
refractive index |
| lambda |
= |
emission wavelength |
| dx |
= |
sampling intervall in x in nm |
| dz |
= |
sampling intervall in z in nm (commonly called
step size) |
You can use the Bitplane Web-Calculator to compute the sampling intervals according to the above formula.
The following Excel-sheets can be used to compute the sampling sizes for a particular optical setting (RI, lambda,...)
The values which we have now calculated are the step sizes in the focus plane of the objective (in the sample space).
Acquisition Using Confocal Microscopy
Most image acquisition software either reports the voxel sizes (in x,y,z) or allows you to measure distances in the image (e.g. you measure the size of the image in x and divide it by the number of voxels in x to get the size of one voxel). You can set the lateral voxel size by changing the objective magnification or the zoom factor (scan area).
The axial sampling distance is achieved by setting the step size of the camera to the ideal sampling value.
Acquisition Using CCD Cameras
The elements of the CCD camera have a defined shape and size. To match the sampling requirements the total magnification has to be chosen such that the sampling size equals the element size divided by the total magnification.
Total Magnification
If the size of the image plate and the resolution (number of pixels) is known, the detector element size can be obtained by the following equation:
elementSize= detectorSize
/ numberOfPixels
The total magnification of the optics is now calculated
by the following formula
mag = elementSize / samplingInterval
The total magnification is the magnification of the objective lens times the magnification of any other lens in the light path.
Example
Using the Hamamatsu C5985 and a 63x/1.4 NA objective lens the calcualtion is as follows:
| |
Optimal Sampling |
|
 |
|
|
| Parameter |
Ideal Value |
Description |
| Sampling Sizes |
91, 91, 270 nm (x,y,z) for 514 nm excitation |
size of one image element |
| Pixel Size on chip |
8.5 micron |
physical size of a single detector
element in a C5985 |
| Total Magnification needed |
93x |
=8500/91 |
| Cmount-Magnification (or optovar) |
1.4 |
=93/63 |
In the above calculation the magnification of the C-mount (intermediate magnification) should be set to 1.4 to achive optimal sampling in the lateral direction. Sampling in the axial direction is done by setting the step size to 270 nm.
Defining the Intensity Range
The above specifications define the spatial sampling. To obtain an optimal volume image the intensity sampling has to be controlled, too. For this it is most important that all the voxel values (voxel intensities) fall into the range of the detector system. To be sure that such a condition has been met we recommend to not use the lowest and the highest pixel value (i.g. 0 and 255 in an 8-bit system). Many data acquisition systems allow you to use a special look-up table which highlights the lowest and highest pixel (voxel) intensity in color.
A detector saturation condition is very critical since the image no longer stores the correct information about a bright emitter which has radiated into the surrounding image. The brightness of such an emitter is underestimated by the system and therefore under-corrected by the deconvolution system.
Recording the Parameters
For a successfull deconvolution the following parameters must be known:
- the numerical aperture of the lens
- the excitation wavelength
- the emission wavelength
- the refractive index of the mounting medium
- the pinhole size (for confocal microscopes only)
- the number of excitation photons (single-photon,
two-photon, ...)
- the sampling sizes (see above)
- the microscopy mode (wide-field or confocal)
|
|
|
