## Microsoft word - phase filters.doc

Phase filters

Object light field distribution function f (x) can be consider as f (x)  g(x)e So far we have discussed filters that deal with amplitude only. Let us consider a “pure” phase object of so that I (x)  f (x)  one cannot “see” the phase variation(x) across the field. Phase contrast viewing

If the phase variations (x) are small compared with unity 1, then f (x)  i (x)  1 i(x)   F ( f )   ( f )  i( f ) where ( f )    which is a real delta function at the origin added to a 90 out-of-phase phase spectrum. If this unfiltered distribution is observed in the image plane, a uniform intensity distribution is all that appears. The phase distribution is not visible. If we introduce a filter in the Fourier plane such that the two terms  ( f ) and ( f ) interact, (x) can be Consider a filter with transmission function where  is a very small distance from the origin. F ( f )  T ( f ) Immediate after the filter the function is F ( f ) T ( f )  [ ( f )  i( f )]T ( f ) i ( f )  i( f )  [i ( f )  ( f )]   [i ( f )  ( f  1  2 (x') Where  (x')  1 and can be ignored. the original phase distribution becomes visible as an intensity distribution added to a bright background (positive phase contrast) Negative phase contrast Similarly if we introduce phase filter with transmission function then the intensity at the image plane is  the original phase distribution becomes visible as an intensity distribution subtracted from the bright
background (i.e. negative phase contrast)
Phase-contrast microscopy (F. Zernike: Zernike filter, Noble price in1953 for physics)
Illumination through two points of an object, due to the difference in thickness, say, may result the same transmitted beam amplitude, through differ in their phase. The phase difference is not “visible”. This is in fact one of the major problems when viewing a transparent object e.g. examination of biological materials under an optical microscope. However if illumination of constant amplitude and phase is superimposed across the field, interference occurs and the resultant transmitted beam are different in amplitude as well as phase. The optical path differences have therefore been made “visible”. One of the simplest arrangements for doing this is as follow: Light is focused on the specimen S by a condenser lens C. A diaphragm D in the form of an annular slot is placed in the front focal plane of C, and its image is formed as a ring of light in the back focal plane of O at P by light that has not been diffracted by the specimen. The phase difference is introduced by means of a phase plate at P consisting of an optically parallel glass plate on which a thin layer of dielectric material has been deposited over the area of the ring, or everywhere except the ring, giving “negative” or “positive” phase contrast respectively. In microscopy: e.g. viewing living squamous cell where most of the materials are transparent. They differ in refractive under the thickness only. By using phase contrast filter they become “visible”. Optical micrographs of squamous cells from the (a) Phase contrast (b) Conventional bright-field illumination

Source: http://ap.polyu.edu.hk/apakhwon/Phase%20filters.pdf

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