Use of the circular Dammann grating in angle measurement

Patterned Photoalignment in Thin Films: Physics and Applications

Photoalignment of liquid crystals by using azo dye molecules is a commonly proposed alternative to traditional rubbing alignment methods. Photoalignment mechanism can be well described in terms of rotational diffusion of azo dye molecules exposed by ultraviolet polarized light. A specific feature of the irradiated light is the intensity dependent change of azimuthal anchoring of liquid crystals. While there are various mechanisms of azo dye photoalignment, photo-reorientation occurs when dye molecules orient themselves perpendicular to the polarization of incident light. In this review, we describe both recent achievements in applications of photoaligned liquid crystal cells and its simulation. A variety of display and photonic devices with azo dye aligned nematic and ferroelectric liquid crystals are presented: q-plates, optically rewritable flexible e-paper (monochromatic and color), and Dammann gratings. Some theoretical aspects of the alignment process and display simulation are also considered.

Note: Comparison experimental results of the laser heterodyne interferometer for angle measurement based on the Faraday effect

A laser heterodyne interferometer for angle measurement based on the Faraday effect is proposed. A novel optical configuration, designed by using the orthogonal return method for a linearly polarized beam based on the Faraday effect, guarantees that the measurement beam can return effectively even though an angular reflector has a large lateral displacement movement. The optical configuration and measurement principle are presented in detail. Two verification experiments were performed; the experimental results show that the proposed interferometer can achieve a large lateral displacement tolerance of 7.4 mm and also can realize high precision angle measurement with a large measurement range.

Light-Driven Liquid Crystal Circular Dammann Grating Fabricated by a Micro-Patterned Liquid Crystal Polymer Phase Mask

As one of the diffractive optical elements, circular Dammann grating has shown its excellent versatility in practical applications. The electrically switchable Dammann grating has been extensively investigated; however, the research on the optically tunable circular Dammann grating has received less attention and reports on this subject have been insufficient in the past decade. In this paper, three-order and eight-order binary-phase liquid crystal circular Dammann gratings with two mutually orthogonal photo-induced alignments in every two adjacent alignment domains, fabricated by a micro-patterned liquid crystal polymer phase mask, are proposed to generate annular uniform-intensity patterns in the far field. A simple maskless optical tuning of an eight-order liquid crystal circular Dammann grating is demonstrated by controlling the polarization of an ultraviolet light as well as the energy dose. The proposed liquid crystal circular Dammann gratings with high efficiencies and desirable uniformities exhibit outstanding optical as well as electrical tunabilities, enabling the widespread prospective applications in adaptive photonic chips stimulated flexibly by only light or by the combination of light and electric field.

Angle measurement with laser feedback instrument

An instrument for angle measurement based on laser feedback has been designed. The measurement technique is based on the principle that when a wave plate placed into a feedback cavity rotates, its phase retardation varies. Phase retardation is a function of the rotating angle of the wave plate. Hence, the angle can be converted to phase retardation. The phase retardation is measured at certain characteristic points identified in the laser outputting curve that are then modulated by laser feedback. The angle of a rotating object can be measured if it is connected to the wave plate. The main advantages of this instrument are: high resolution, compact, flexible, low cost, effective power, and fast response.

Circular Dammann grating under high numerical aperture focusing

Circular Dammann grating (CDG) under high numerical aperture (NA) focusing is described based on Richards-Wolf vectorial diffraction theory in this paper. Several CDGs are presented under the condition of NA=0.9 with the illumination of circularly polarized plane-wave laser beams. Numerical results show that the sizes of these circular patterns with equal-intensity are in the wavelength scale, and doughnut-shaped central spots and dark rings are in the subwavelength width. To verify this kind of CDG, a binary pure-phase three-order CDG is fabricated to produce a dark center pattern surrounded by three concentric bright rings. The corresponding intensity distribution of the pattern on the focal plane of a high-NA objective (NA=0.9) is measured, and the results agree well with theoretical simulations. This kind of CDG with annular patterns of equal-intensity in the wavelength scale should be highly interesting for its potential applications in optical trapping, stimulated emission depletion (STED) microscopy, and the study of singular optics, as well as annular array illumination.

Circular Fibonacci gratings

We introduce circular Fibonacci gratings (CFGs) that combine the concept of circular gratings and Fibonacci structures. Theoretical analysis shows that the diffraction pattern of CFGs is composed of fractal distributions of impulse rings. Numerical simulations are performed with two-dimensional fast Fourier transform to reveal the fractal behavior of the diffraction rings. Experimental results are also presented and agree well with the numerical results. The fractal nature of the diffraction field should be of great theoretical interest, and shows potential to be further developed into practical applications, such as in laser measurement with wideband illumination.

Polarization-dependent circular Dammann grating made of azo-dye-doped liquid crystals

A polarization-dependent circular Dammann grating (CDG) was generated from an azo-dye-doped liquid crystal (LC) cell. A simple multiexposure photo-alignment process was used to fabricate a binary phase LC CDG zone plane, which was composed of an odd zone with a twisted nematic LC structure and an even zone with a homogenous LC structure. A two-order CDG with equal-intensity rings was produced through a Fourier transform. The maximum zeroth and first diffraction orders of obtained CDG can be separately achieved by rotating the analyzer's polarization direction. The CDG using an azo-dye-doped LC cell can be used to generate diffractions by lasers in a broad wavelength range, hence expanding possible device applications.

Three-dimensional complex image coding using a circular Dammann grating

Recently, optical image coding using a circular Dammann grating (CDG) has been proposed and investigated. However, the proposed technique is intensity based and could not be used for three-dimensional (3D) image coding. In this paper, we investigate an optical image coding technique that is complex-amplitude based. The system can be used for 3D image coding. The complex-amplitude coding is provided by a circular Dammann grating through the use of a digital holographic recording technique called optical scanning holography. To decode the image, along the depth we record a series of pinhole holograms coded by the CDG. The decoded reconstruction of each depth location is extracted by the measured pinhole hologram matched to the desired depth. Computer simulations as well as experimental results are provided.

Area measurement at long-distance using a circular Dammann grating

We describe a novel method of noncontact mode area measurement at long distance of 11.25 m by borrowing the concept of a circular Dammann grating (CDG). The area of objects can be determined accurately by measuring the circular spectrum diameter of the CDG. This noncontact mode measurement requires neither a large amount of image data nor any pattern recognition approach. The spectrum diameter is derived from simple lens formulas. From the fractional Fourier transform, we find that there exists a linear relationship between the spectrum diameter and the distance traveled by the CDG. Compared with the conventional methods, this technique has the advantages of a simple design with good accuracy of better than 3%, low cost, noncontact mode, and a more compact design. Finally, we present several experimental results demonstrating the effectiveness of this system.