טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentVander Roman
SubjectFourier Fringe Analysis with Improved Spatial Reslosoution
DepartmentDepartment of Physics
Supervisor Professor Emeritus Stephen Lipson


Abstract

The spatial resolution of the phase image derived from the interferogram by Fourier fringe analysis is limited by the necessity to isolate a first order in the Fourier plane.

As it will be shown, several problems occur using this method. The accuracy to which the phase can be measured depends on the size of the Fourier-plane window used to select the order. The bigger the window, the better the spatial resolution is, but if it is made too large, information from the rejected orders of the transform enters and results in phase errors. There is therefore a trade-off between accuracy of phase determination and spatial resolution.

            In this thesis we propose and demonstrate experimentally a new method of improving the spatial resolution without losing phase accuracy. It utilizes the fact that every two-beam interferometer has two complementary output fields, of which only one is generally used. By using the two complementary outputs of the interferometer, it is possible to eliminate the zero order by subtracting the FFT patterns of images recorded by CCDs at two interferometer exits. This now allows us to use a Fourier plane window that is two times bigger than in the ordinary technique, and thus to improve the spatial resolution by a factor of two.

The phase accuracy in both methods is the same and is about 0.01 rad. We have also shown that even if the maximal spatial carrier frequency is used it is impossible to reach (in an ordinary FFA) a minimal sample detail in the reconstructed pattern that is smaller than 2 pixels. In our technique using two interferometer exits and subtracting their FFT patterns the 1 CCD pixel limit can be achieved.


The theory of this improvement is presented and confirmed experimentally.