Maciej Sypek

Light propagation in the Fresnel region. New numerical approach

Abstract The paper presents the comparison of light propagation simulation methods in the Fresnel region. The theoretical approach is based on the Kirchhof scalar theory of diffraction. In the case of the complex amplitude calculated by using the spectrum of the plane waves a new approach is included. Advantages and disadvantages of the presented methods are compared and discussed. The simulated results are verified in an experimental optical setup.

Imaging with extended focal depth by means of lenses with radial and angular modulation

The paper presents imaging properties of modified lenses with the radial and the angular modulation. We analyze three following optical elements with moderate numerical apertures: the forward logarithmic axicon and the axilens representing the radial modulation as well as the light sword optical element being a counterpart of the axilens with the angular modulation. The abilities of the elements for imaging with extended depth of focus are discussed in detail with the help of structures of output images and modulation transfer functions corresponding to them. According to the obtained results only the angular modulation of the lens makes possible to maintain the acceptable resolution, contrast and brightness of the output images for a wide range of defocusing. Therefore optical elements with angular modulations and moderate numerical apertures seem to be especially suitable for imaging with extended focal depth.

Simple holographic projection in color

Extremely simplified image projection technique based on optical fibers and a single Spatial Light Modulator is presented. Images are formed by addressing the modulator with especially iterated Fourier holograms, precisely aligned on the projection screen using phase factors of lenses and gratings. Focusing is done electronically with no moving parts. Color operation is done by spatial side-by-side division of the area of the modulator. Experimental results are given, showing good image quality and excellent resistance to obstructions in the light path. Speckles are suppressed by micro-movements of the screen and by time-averaging of a number of holograms into the final image.

Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation

A new effect during light propagation simulation in the Fresnel region is discovered. Image multiplying and high-frequency noise effects are caused by the sampling of the complex light field. Image multiplying is observed in the case of the standard integral calculation. High-frequency noise is observed in the convolution approach. These effects are observed in a computer simulation only and do not exist in nature. The analysis of these effects enable us to define the range of the numerical algorithms application.

Diffractive elements for imaging with extended depth of focus

We present the abilities of diffractive elements for imaging with extended depth of focus. The elements of interest belong to the class of diffractive structures focusing incident light into a segment of the optical axis. We describe the imaging properties of the two following elements of this kind: the annular axicon and the light sword optical element (LSOE). In particular, the point spread functions and the modulation transfer functions of axicons and LSOEs are analyzed experimentally and numerically in detail. The obtained results correspond to different defocusing parameters. The performed experiments confirm the usefulness of axicons and LSOEs for imaging with extended depth of focus.

Three-plane phase-only computer hologram generated with iterative Fresnel algorithm

A novel iterative method of generating three-plane, phase-only computer-generated holograms is presented. It is based on the iterative Fresnel ping-pong two-plane algorithm. A modification is introduced to extend the method for three planes, i.e., two object planes and a hologram itself. The described method enables the design of low-noise and high-efficiency phase-only holograms using a numerical Fresnel propagation algorithm. The source method is described, followed by the modified algorithm. Numerical simulation results and algorithm parameters are discussed, followed by a discussion of the method limitations.

The Light Sword Optical Element—a New Diffraction Structure with Extended Depth of Focus

Abstract This letter introduces a novel diffraction structure, the light sword optical element, with extended depth of focus.

Color image projection based on Fourier holograms

A method of color image projection is experimentally validated. It assumes a simultaneous illumination of a spatial light modulator (SLM) with three laser beams converging in a common point on a projection screen. The beams are masked with amplitude filters so that each one illuminates one third of the area of the SLM. A Fourier hologram of a chosen color component of an input image is calculated, and its phase pattern is addressed on a corresponding part of the SLM area. A full-color flat image is formed on the screen as a result of color mixing. Additional techniques of image optimization are applied: time-integral speckle averaging and an off-axis shift of a zero-order peak. Static and animated experimental results of such a color holographic projection with a good image quality are presented.

Colorful reconstructions from a thin multi-plane phase hologram

A new technique of design and reconstruction of a color hologram is presented. The design is based on an iterative multi-plane optimization algorithm. It allows to encode three different images for a reconstruction at various distances measured from the hologram plane. The distances are calculated in order to obtain a fine color compound image when the hologram is illuminated by three laser beams of RGB colors. A single light phase modulator is used instead of three. The reconstructed red, green and blue component images remain in an exact match in size and position. The 2-D color image is reconstructed at a pre-assumed distance and its color pattern can be easily controlled by the choice of the three input component images.

Experimental evaluation of a full-color compact lensless holographic display

An iterative phase retrieval method for a lensless color holographic display using a single light modulator is experimentally validated. The technique involves iterative calculation of a three-plane synthetic hologram which is displayed on a SLM simultaneously lit with three laser beams providing an RGB illumination. Static and animated two-dimensional flicker-free full color images are reconstructed at a fixed position and captured using a high resolution CMOS sensor. The image finesse, color fidelity, contrast ratio and influence of speckles are evaluated and compared with other techniques of holographic color image encoding. The results indicate the technique superior in a case of full-color real-life pictures which are correctly displayed by this ultra-compact and simple projection setup.