Optical implementation of a wavelet transform by the use of dynamic holographic recording in a photorefractive material

Optical nonsubsampled contourlet transform

The nonsubsampled contourlet transform (NSCT) is a fully shift-invariant, multiscale, and multidirectional expansion implemented in optics using the Fourier transform of its filters. In this paper, we propose a novel optical NSCT filter design method and the corresponding post-processing method to avoid the use of holographic techniques. The novel optical NSCT filter has real and non-negative Fourier transforms. The input image is placed in the input plane of the VanderLugt 4f correlator, and these real and non-negative Fourier transform NSCT filters are placed in the frequency plane of the VanderLugt 4f correlator. Next, the NSCT result is captured by a CCD in the output plane of the VanderLugt 4f correlator, and its perfect reconstruction is theoretically possible, which is demonstrated by both simulation and optical experiment.

Semiconductor CdF₂:Ga and CdF₂:In Crystals as Media for Real-Time Holography

Monocrystalline cadmium fluoride is a dielectric solid that can be converted into a semiconductor by doping with donor impurities and subsequent heating in the reduction atmosphere. For two donor elements, Ga and In, the donor (“shallow”) state is a metastable one separated from the ground (“deep”) state by a barrier. Photoinduced deep-to-shallow state transition underlies the photochromism of CdF₂:Ga and CdF₂:In. Real-time phase holograms are recorded in these crystals capable of following up optical processes in a wide frequency range. The features of photochromic transformations in CdF₂:Ga and CdF₂:In crystals as well as holographic characteristics of these media are discussed. Exemplary applications of CdF₂-based holographic elements are given.

One-way imaging through a polarization-sensitive aberrator by use of an optical lock-in detection

We demonstrate one-way image compensation for a thin and polarization-sensitive aberrator by the use of optical lock-in detection. Optical lock-in detection is accomplished by dual-phase modulation in four-wave mixing in a holographic medium. In our scheme, both the image-bearing beam and the reference beam copropagate through the aberrator under the same polarization condition. The holographic grating that reconstructs only the corrected image was generated by selective recording in optical lock-in detection. The phase aberration is subtracted out in the holographic process. This scheme permits image correction through the polarization-sensitive aberrator.

Hologram reconstruction by use of optical wavelet transform

High-speed in-line holography is used to visualize the trajectories of glass fibers being drawn out in a turbulent flame. To improve the signal-to-noise ratio, the images are not observed by a conventional reconstruction setup, but the holographic plate is placed directly on the input plane of a wavelet-transform optical system. This processing system is based on a VanderLugt correlator with inclusion of an electrically addressed spatial light modulator. The shape of the matched filters is deduced by successive rotation and dilatation operations of wavelet functions in the Fourier domain. We estimate the three-dimensional location of a fiber element and its orientation by searching for the daughter wavelet that yields the maximum intensity on the output plane of the correlator, which also contains the reconstructed image. The results are compared with those obtained by conventional optical reconstruction. The signal-to-noise ratios of the images observed on the output plane are improved. Moreover, it is shown that the axis coordinate accuracy is improved to Dz = +/-50 microm, instead of +/-0.5 mm for holographic reconstruction.