Depth of Field needed for Fraunhofer Pattern

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Depth of Field (DOF) for a lens is defined as the maximum allowable defocus for a clear Fraunhofer Pattern, but it is not a fixed property since perfect focus occurs at a single plane. The DOF is influenced by the lens's f-number or numerical aperture (NA), with a general formula of DOF = 2 * wavelength * n / NA^2 in the paraxial limit. For lenses with larger numerical apertures, such as those used in microscopy, this formula is adjusted. Additionally, achieving the Rayleigh criterion requires aberrations to be less than one-quarter wavelength. Understanding these principles is crucial for applications requiring precise optical performance.
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Say we define Depth of Field, DOF, as max de-focus allowed for decent Fraunhofer Pattern. Then what's the DOF of a (positive) lens with focal length f?
 
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The DOF is not a well-defined property of a lens, since perfect focus is achieved only at a single plane, and all other distances contain defocus.

However, some 'rules of thumb' exist, similar to the Rayleigh criterion being satisfied if the aberrations are less than 1/4 wavelength. The DOF is set by the f/# or equivalently the numerical aperture of the lens, and in the paraxial limit is given by DOF = 2* wavelength * n/NA^2. For larger numerical apertures (i.e. microscopy), the formula is slightly modified.

http://www.microscopyu.com/articles/formulas/formulasfielddepth.html
 

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