Wavefront Coding

							WAVE-FRONT CODING:
A NEW PARADIGM FOR IMAGING SYSTEMS
W. Thomas Cathey and Edward R. Dowski
W. T. Cathey is with the Department of Electrical and Computer Engineering,
University of Colorado.
E. R. Dowski is with CDM Optics, Incorporated, 4001 Discovery Drive, Suite 2110,
Boulder, Colorado 80303-7816.
          Traditional Imaging Systems


                     In Focus




Objects      Lens
                      CCD




                                Output Image
          Traditional Imaging Systems


                      Out of Focus




Objects      Lens        CCD




                                     Output Image
                                              Wave-front Coding



                                                                Intermediate Image
  Objects
              Wave-front Coding
              Optical Element         Lens           CCD             Image
                                                                   Processing



E. R. Dowski, Jr., and W. T. Cathey,
“Extended depth of field through wave-front coding,” Appl.
Opt. 34, 1859–1866 1995.
Imaging Systems Laboratory, Department of Electrical
Engineering, University of Colorado, Boulder, Colorado 80309.
                                                                  Output Image
   Traditional Imaging System      Wave-front Coding Imaging System




Object     Lens        CCD      Object      Lens       CCD
                                 Wave-front Coding
                                 Optical Element
   Traditional Imaging System      Wave-front Coding Imaging System




Object     Lens        CCD      Object      Lens       CCD
                                 Wave-front Coding
                                 Optical Element
Traditional Imaging System           Wave-front Coding Imaging System



                    In Focus                               In Focus




 Out of Focus CCD                       Out of Focus CCD




                       In Focus                             In Focus

 PSFs                                  PSFs

                      Out of Focus                          Out of Focus
                                     H

                                   System
Impulse                                                             PSF

          Input Signal                              Output Signal




                     In Focus                                       In Focus

PSFs                                         PSFs

                    Out of Focus                                    Out of Focus


Traditional Imaging System                  Wave-front Coding Imaging System
Ambiguity Function A(u,v)   Phase Function P(x)




u: Spatial Frequency
ψ: Misfocus Parameter
              Spatial Frequency

       Low



Spatial
Frequency


       High
Modulation Transfer Functions
                       (MTFs)
  Wave-front Coding Imaging System



                                                          PSFs

Object       Lens        CCD
                                     Intermediate Image
 Wave-front Coding
 Optical Element
         Phase Surface                    Image
                                        Processing    Weiner Filter




                                       Output Image
  Wave-front Coding Imaging System



                                                          PSFs

Object      Lens        CCD
                                     Intermediate Image
 Wave-front Coding
 Optical Element

                                          Image
            Weiner Filter               Processing




                                       Output Image
                             Why Wave-front Coding?

         Wave-front




Object                Lens         CCD




         Wave-front




Object                Lens        CCD
Applications:
Extended Depth of Field Imaging

                Traditional System Image




                Extended Depth of Field Image




                Traces through both images
Applications:
Extended Depth of Field Imaging




W. T. Cathey and E. Dowski, “A new paradigm for imaging systems,”
Appl. Opt. 41, 6080 (2002).
 Applications: Actuator Images




                                Traditional Image




(a-d)Traditional Image       Wave-front Coded Image
(e) Wave-front Coded Image
Applications:
Fluorescence Imaging




 Traditional System Image   Wave-front Coded Image
Applications:
Achromatic Imaging




                  Traditional
                 System Image




                     Wave-front
                      Coded
                       Image
Kenneth Kubala, Edward Dowski, and W. Cathey ,”Reducing complexity
in computational imaging systems,” Optics Express, Vol. 11, Issue 18, pp.
2102-2108
Applications:
Liquid Lens with Wave-front Coding
Chir-Weei Chang and Yung-Lin Chen “Using liquid lens in
wavefront coded imaging system,” Proc. SPIE, Vol. 7061,
70610O (2008); DOI:10.1117/12.794930 .
Images of Liquid Lens System
                               Images of Liquid Lens
                               System with
                               Wavefront Coding