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Spot Image Size Using Focal Length

If two objects imaged by a camera are separated by an angle small enough that their Airy disks on the camera detector start overlapping, the objects cannot be clearly separated any more in the image, and they start blurring together. The closest separation of the images of two objects on the film before significant blurring occurs is the spot image size.

The spot image diameter divided by the focal length is proportional to the light wavelength divided by the diameter of aperture.

Formula

QuantityVariable["d", "Diameter"]/QuantityVariable["f", "Length"] == (2*BesselJZero[1, 1]*QuantityVariable["λ", "LightWavelength"])/(Pi*QuantityVariable["D", "Diameter"])

symbol description physical quantity
d spot image diameter "Diameter"
f focal length "Length"
D diameter of aperture "Diameter"
λ light wavelength "LightWavelength"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Spot Image Size Using Focal Length"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Spot Image Size Using Focal Length"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Spot Image Size Using Focal Length"], {QuantityVariable[ "f","Length"] -> Quantity[50, "Millimeters"], QuantityVariable["\[Lambda]","LightWavelength"] -> Quantity[530, "Nanometers"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1835

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