Optical transfer function: Difference between revisions

Revision as of 12:45, 23 June 2019

Revision as of 19:13, 11 July 2019

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== Calculation ==

Most [[Optical lens design|optical design software]] has functionality to compute the optical or modulation transfer function of a lens design. Ideal systems such as in the examples here are readily calculated numerically using software such as [[Julia (programming language)|Julia]], [[GNU Octave]] or [[Matlab]], and in some specific cases even analytically. The optical transfer function can be calculated following two approaches:<ref name=Goodman2005>{{cite book |first=Joseph|last=Goodman|year=2005|title=Introduction to Fourier Optics|edition=3rd ed,|publisher=Roberts & Co Publishers|isbn=0-9747077-2-4}}</ref>

# as the Fourier transform of the incoherent [[point spread function]], or

# as the auto-correlation of the [[pupil function]] of the optical system

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=== The vectorial transfer function ===

At high numerical apertures such as those found in microscopy, it is important to consider the vectorial nature of the fields that carry light. By decomposing the waves in three independent components corresponding to the Cartesian axes, a point spread function can be calculated for each component and combined into a ''vectorial'' point spread function. Similarly, a ''vectorial'' optical transfer function can be determined as shown in <ref name=Sheppard1997>{{Cite journal | last1 = Sheppard| first1 = C.J.R. | last2 = Larkin | first2 = K. | title = Vectorial pupil functions and vectorial transfer functions | journal = OPTIKOptik-STUTTGARTStuttgart | volume = 107 | pages = 79–87 | year = 1997 | pmid = | pmc = | url = http://www.nontrivialzeros.net/KGL_Papers/28_Vectorial_OTF_Optik_1997.pdf}}</ref> and

.<ref name=Arnison2002>{{Cite journal | last1 = Arnison | first1 = M. R. | last2 = Sheppard | first2 = C. J. R. | doi = 10.1016/S0030-4018(02)01857-6 | title = A 3D vectorial optical transfer function suitable for arbitrary pupil functions | journal = Optics Communications | volume = 211 | issue = 1–6 | pages = 5353–63 | year = 2002 | pmid = | pmc = | url = http://www.purplebark.net/mra/research/votf/|bibcode = 2002OptCo.211...53A }}</ref>

== Measurement ==