Where Does the 0.61 in the Diffraction Limit Formula Come From?

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SUMMARY

The discussion centers on the origin of the constant 0.61 in the diffraction limit formula, specifically in the context of microscopy. The formula used is d = (0.61 × wavelength) / NA, where d represents the diffraction-limited spatial resolution, wavelength is 660 nm for red light, and NA is the numerical aperture of 0.90. The calculated spatial resolution is 447 nm, derived from a focal length of 1.8 mm for the microscope objective. The constant 0.61 is a factor that arises from the mathematical derivation of diffraction limits in optical systems.

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  • Understanding of numerical aperture (NA) in microscopy
  • Familiarity with the concept of diffraction limits
  • Knowledge of wavelength and its role in optical systems
  • Basic principles of optical microscopy and lens calculations
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This discussion is beneficial for optical engineers, microscopy researchers, and anyone involved in the design and application of optical systems in scientific research.

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An infinity corrected microscope objective has a magnification of 100× for a tube lens
with focal length 180 mm. The numerical aperture of the objective is 0.90. Calculate the
the diffraction limited spatial resolution if the objective is
used with red light (660 nm). (Ans.: f=1.8 mm; d=447 nm)

Note I have already calculated the focal length of the objective lens as 1.8mm.

The answer reads d=(0.61*wavelength)/NA
A=aperture Can someone please tell me where the number 0.61 is coming from?

Thanks
 
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