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How much resolution? How wide a field-of-view?

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
Effective pixels Active pixels, Resolution
Cell size Pixel size
Effective area Image area, Active area, Sensor/diagonal
Field-of-view

Reading a camera specifications table can involve not only having to translate from engineering into biology, but from the language of one camera manufacturer to another. This is particularly true of the terms that go into describing how much resolution is achievable.

Field of view

Let’s start with the terms effective pixels, active pixels, and resolution. These all refer to the number of pixels that go into capturing an image—the square or rectangular grid that you can lay over your image, where each pixel reports on photons captured over a specific area (see figure below).

The area of the image that each pixel covers depends on the size of the pixel and is listed in the specifications table as cell size or pixel size.

Multiplying the cell/pixel size by the number of pixels converts the field-of-view captured in a single image from pixels to millimeters, and is listed as effective area, image area, active area, or sensor format/diagonal.

Why are the number of pixels described as effective pixels or active pixels instead of simply pixels? The words effective and active are used to remove any ambiguity on exactly how many pixels are actually used to capture an image—for some cameras not all the pixels on the sensor contribute to the image, but rather are used for transferring or holding photoelectrons or voltage.

Resolution

How does the pixel size spec translate into camera resolution?

For starters, it’s important to bear in mind that the optical system limits resolution—if the microscope can’t resolve the image then the camera will not be able to see it either. So we begin by looking at microscope resolution and calculating the size of the projected image of the object to be resolved. And to do this, we need to first define what we mean by resolution.

How is resolution defined?

In 1873, the physicist Ernst Abbe first defined the diffraction limit of an objective as l/2NA. Lord Rayleigh later refined this equation for microscopes to be 0.61 x l/NA—the separation necessary to distinguish two Airy patterns as separate objects.

From Rayleigh’s equation we can calculate the size of the smallest item the objective can resolve, and when this number is multiplied by the magnification of the objective (assuming no additional intermediate optics) we can calculate how large the item will appear to be when it is projected onto the camera’s sensor.

What size pixels do I need to see this level of resolution?

Now that we have determined the resolution of the optical system and the projected size of objects, we can determine the maximum acceptable pixel size needed to meet this resolution. The question becomes one of sampling—given the need to fulfill the Nyquist criteria, which provides a theoretical framework for the minimum number of pixels needed to accurately define an object, we need to ensure that the object of interest is projected on to at least two pixels on the camera sensor (ideally more, 2.5 to 3 is recommended for high resolution microscopy.)

As an example, we’ll imagine trying to resolve peroxisomes from rat liver parenchymal cells that are roughly 0.7 μm in diameter. To resolve a 0.7 μm object, we’d need an objective of similar or higher resolution. From Table 1, the minimum magnification needed would be the objective with10x magnification and an NA of 0.45 (of course, if a wide field-of-view is not needed, most microscopists would oversample and use a higher magnification to achieve a more visually pleasing and informative image). At this magnification, the projected image would be 7.5 μm, so we’d need a camera with a pixel size of 7.5 μm / 2 = 3.7 μm or smaller.

Table 1.
Objective Numerical Aperture (NA) Resolution Limit*(Rayleigh’s criterion) (μm) Projected Size (μm) Maximum Acceptable Pixel Size (μm)
4 0.20 1.7 6.7 3.4
10 0.30 1.1 11.2 5.6
10 0.45 0.7 7.5 3.7
20 0.50 0.7 13.4 6.7
20 0.75 0.4 8.9 4.5
40 0.75 0.4 17.9 8.9
40 1.30 0.3 10.3 5.2
60 1.40 0.2 14.4 7.2
100 1.30 0.3 25.8 12.9
100 1.40 0.2 24.0 12.0
*Assume 550 nm light
BOTTOM LINE:
  • The field-of-view that a camera is able to deliver is reflected in the terms effective pixels, cell size, and effective area or their equivalents at each manufacturer.
  • If the microscope cannot resolve the smallest feature you care about, the camera cannot either.
  • After determining that your microscope can resolve the object of interest, you need to determine that you are sampling the image at a high enough frequency (with enough pixels) at the camera.
  • When determining if your camera can meet your sampling needs, ensure that the projected image size will span more than two pixels (i.e. touches at least parts of three pixels).

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