Fringe Pattern Normalization Using Bidimensional Empirical Mode Decomposition and the Hilbert Transform

MARÍA BELÉN BERNINI; ALEJANDRO FEDERICO; GUILLERMO H. KAUFMANN

Nürtingen, Alemania

Congreso; Fringe '09, the 6th International Workshop on Advanced Optical Metrology; 2009

Institut für Technische Optik

The Empirical Mode Decomposition  (EMD)  is a nonlinear method  that was developed  in  the  last decade for adaptively representing a non-stationary signal as a sum of zero-mean well-behaved fast and slow oscillation modes referred  to as Intrinsic Mode Functions (IMFs). This decomposition  is carried out  through a  sifting process which generates a  fully data-driven method,  so  that no basis functions are fixed in the analysis process. Consequently, the evaluation of the performance of the EMD method in a given field must be analysed by means of numerical analysis.  Even though the EMD method has been successfully used during the last few years in several fields, its  application  in  speckle  metrology  is  almost  new.  Quite  recently,  the  one  dimensional  EMD method  was  applied  with  promising  results  to  denoise  speckle  fringes  and  also  to  improve  the evaluation  of  phase  distributions  in  temporal  speckle  pattern  interferometry.  More  recently,  a bidimensional Empirical Mode Decompostion  (BEMD) algorithm was proposed  in order  to adapt the EMD method to the decomposition of speckle fringe patterns.  In this paper, the application of the BEMD method to normalize fringe patterns is investigated. We show  that  the application of  the BEMD approach  to  a  fringe pattern  tends  to  locally  separate  the spatial  frequency  components  of  the  image.  This  property  motivated  the  development  of  a normalization algorithm. To obtain such a procedure, we first present and discuss a bidimensional extension of the original EMD approach. The main drawbacks of the BEMD method are related to the  definitions  of  the  extrema  of  the  speckle  fringe  image  and  the  selection  of  the  interpolation method  to be applied  to  these points.  In addition,  the decomposition  in 2D  is  time consuming,  so that a special strategy to reduce the processing time must be used. Particular attention is devoted to the  boundary  conditions  of  the  fringe  pattern  analysis.  With  the  introduction  of  various improvements, it is shown that  the proposed BEMD method can separate the background intensity immersed  in  the  fringe  pattern.  Using  an  additional  technique  implemented  via  the  Hilbert transform, it is also possible to take into account the modulation intensity variations. To evaluate  the performance of  the proposed normalization procedure, computer generated  fringe patterns with background and modulation intensity variations were generated. The main advantage of  synthetic  fringes  over  experimental  ones  is  that  the  intensity  variations  are  known  precisely. Then,  the  resulting  normalized  fringe  pattern  can  be  compared with  the  original  one.  Finally,  a comparison with other well established normalization procedures is also presented.