Frank Wyrowski

Iterative Fourier-transform algorithm applied to computer holography

In the generation of computer-generated holograms the phase is in many applications a free parameter that can be manipulated to achieve a high diffraction efficiency, a small space–bandwidth product, and a speckle-free reconstruction. An iterative algorithm to determine such phase distributions is described. Experimental verifications are given.

Diffractive optical elements: iterative calculation of quantized, blazed phase structures

A procedure to calculate a highly quantized, blazed phase structure is presented. Characteristics that are concentrated on are a high diffraction efficiency and a large signal-to-noise ratio. The calculation techniques are based on iterative Fourier-transform algorithms. Stagnation problems are discussed, and methods to overcome them are described.

Fast calculation method for optical diffraction on tilted planes by use of the angular spectrum of plane waves

A novel method for simulating field propagation is presented. The method, based on the angular spectrum of plane waves and coordinate rotation in the Fourier domain, removes geometric limitations posed by conventional propagation calculation and enables us to calculate complex amplitudes of diffracted waves on a plane not parallel to the aperture. This method can be implemented by using the fast Fourier transformation twice and a spectrum interpolation. It features computation time that is comparable with that of standard calculation methods for diffraction or propagation between parallel planes. To demonstrate the method, numerical results as well as a general formulation are reported for a single-axis rotation.

I Digital Holography – Computer-Generated Holograms

Publisher Summary This chapter describes the digital holography and the computer-generated holograms (CGH). Optical holography is a two-step process: (1) the interferometric recording of a wavefield in a hologram and (2) the reconstruction of the wavefield stored in the hologram by diffraction. In digital holography, the hologram recording step is performed synthetically supported by digital computer means, and the reconstruction step remains the same as in optical holography. CGHs function as diffractive elements in optical systems, and the desired requirements are the same as in the IC-mask and pattern production field. The advantages in this field are directly applicable to the materialization of CGHs. CGH structure implementation by using ablating processes, such as etching, embossing or burning, on surfaces of the transparent and reflective materials have attractive and desirable features. Some of these techniques are combined with an accessory process, such as coating with a light-sensitive film (photo-lac, photo-resist), which is common in lithography.

Digital holography as part of diffractive optics

An essential aspect of digital diffractive optics is the inverse problem of how to proceed from the desired wavefield in space to the design of a diffractive element that is able to form this field. This subject is treated by considering various approximations that define digital holography as a subset of diffractive optics. Analysis and models of inverse wave propagation are presented for boundary conditions determined by the type of material, the fabrication technique and the application. Coding theory is a central topic in the examination of this situation. Coding methods and the prediction of the efficiency of the diffraction are discussed. Nonlinear methods are used to treat the optimization problems. It is shown how diffractive elements can be designed by applying iterative and non-iterative methods. Diffractive elements of different kinds are presented and illustrated. The model examined seems to be of value in treating various ingredients of digital diffractive optics.

Partially coherent Gaussian pulses

The concept of a plane-wave pulse with a Gaussian spectrum and a Gaussian distribution of correlations between different frequency components is introduced. The temporal coherence properties of such a pulse are related to the spectral coherence properties and equivalence relations between pulses with different spectral and temporal correlation parameters are established.

Diffusers in digital holography

In Fourier and Fresnel holography diffuse illumination is used to smooth the power spectrum of the object wave. A speckle pattern will then disturb the diffraction pattern. We present methods to calculate appropriate diffusers in digital holography that do not introduce speckle. The considerations include deterministic object-independent as well as iteratively calculated object-dependent diffusers. Object-independent diffusers are suited for initial phases to avoid stagnation of the iterative procedure.

Iterative quantization of digital amplitude holograms.

An iterative concept is suggested to quantize digital amplitude holograms. It is based on an iterative Fourier transform algorithm. A stepwise introduction of the quantization constraint results in a convergent algorithm. The production of holograms is described and their optical reconstructions are presented.

Study on polarizing visible light by subwavelength-period metal-stripe gratings

One method for influencing the polarization of light is the use of wire-grid polarizers. For the visible region, this type of element can be realized as a metal-stripe grating with periods less than the wavelength. We fabricate metal-stripe gratings with periods down to 190 nm in thin chromium layers of 35-nm thickness using electron-beam lithography and ion-beam etching. A detailed investigation of the influence of grating period and duty cycle on the polarization effect is carried out to verify the conformity of rigorous diffraction theory and experimental results. The comparison between the two indicates good performance. Polarization ratios of the order of 5 with transmission efficiencies of about 60% in TM polarization are obtained. The connection of the polarization effect real- izable and the fabrication technology used is discussed.

Upper bound of the diffraction efficiency of diffractive phase elements

An upper bound of the diffraction efficiency of diffractive elements that only influence the phase of the illumination wave is derived. The derivation only utilizes the specification of the desired diffraction pattern. It is independent of the technique to design and fabricate the diffractive element. The theory is based on the transmittance approach to describe the effect of the element on the illumination wave.