Digital complex holography using a shearing interferometer: principles and early results

Abstract

With the development of high-resolution CCD cameras, digital holography was made possible and has been used in laser metrology 1 . A reference wave interferes with the object wave and an amplitude hologram is formed and digitally recorded on the high-resolution camera CCD. The object intensity and phase information is numerically reconstructed. In this work a different approach is introduced. A digital complex hologram of the object wave is determined without an explicit reference wave. In order to do that, a shearing device is introduced in front of the CCD of a high-resolution camera. A phase shifting device is also used to change the relative phase between each shearing pair. Twelve different images are acquired: (a) four 90 degree(s) phase-shifted images without shearing, (b) four with shearing in the x direction and (c) four with shearing in the y direction. Those images are combined and three phase difference maps are calculated: (a) the phase difference between the two wave fronts without shearing, (b) the phase difference between two neighbor pixels in the x direction and (c) the phase difference between two neighbor pixels in the y direction. To compute the complex hologram, the amplitude and phase values for each pixel must be determined. An initial arbitrary phase value is assigned to a seed point of the image. The phase values of the next neighbor pixels are propagated using the available three phase difference maps and an appropriate algorithm. The digital complex hologram is used to reconstruct the object wave. The intensity and phase patterns are numerically computed in the object plane in a way similar to conventional digital holography. This work presents the mathematical models to compute the digital complex hologram and its numerical reconstruction. In addition, a very early application of digital complex holography to record and reconstruct a point source is presented.