Mao-Hong Lu

Double-diffraction planar encoder by conjugate optics

A planar encoder using conjugate optics is proposed for sens- ing the 2-D displacement of a 2-D grating. A Doppler frequency shift of diffracted light is generated when the grating moves. The optical conju- gate path can compensate for the error arising from the relative tilt be- tween the optical head and the scale (head-to-scale tilt). Additionally, the optical head is easily integrated, having high tolerance in component-to- component placement. The 2-D displacement system with the 2-D grat- ing, which has period of 1.6 mm in both the X and Y directions, provides a signal period of 0.4 mm by using a double-diffraction configuration. This system and associated electronics provide interpolation with a factor of 400, corresponding to a measurement resolution of 1 nm.

Two-optical-component method for designing zoom system

A new method is presented to solve a zoom system in which the lenses are divided into two combined units, and each combined unit is defined as an optical component. It is shown that most zoom systems can be considered as two-component systems and can be solved using principal plane techniques of optical component, and the first-order zoom system design is thus made easier. The theory with some examples are described.

High resolution planar encoder by retro-reflection

This investigation presents a planar diffractive laser encoder system (PDLENS), which serves as a two-dimensional (2D) position detection apparatus for precision machine applications. Traditional 2D position detection utilizes a pair of linear encoders in crossed construction and so maintaining the perpendicularity between this pair of encoders is difficult. Besides, the rigorous alignment requirements among various components of the encoder system impose a serious user adaptation bottleneck. Of all alignment tolerances, the head-to-scale alignment tolerance is the most important problem for applications. In this work, a 2D grating is employed as the scale and the PDLENS is based on the retro-reflection configuration. Therefore the new encoder can provide good perpendicularity and tolerate larger alignment errors than the conventional encoder does. The grating pitch is 1.6μm and the period of the output signal is 0.4μm due to the double diffraction. Electronic interpolation with a factor of 400 leads to a...

First‐order analysis of a two‐conjugate zoom system

A general analysis for the first-order design of the two- conjugate zoom system, which consists of three lenses and has a real or virtual image, is presented. The design formulas are derived. Of two- conjugate zoom systems, we analyze the solution areas in the system parameter diagrams under two particular initial conditions in which the object/image and pupil magnifications of the middle lens are taken to be 1 and 2 1o r 21 and 1. Two design methods are proposed. Several examples are given to demonstrate the proposed design procedures.

Method of solving triplets consisting of a singlet and air-spaced doublet with given primary aberrations

Abstract An effective algebraic algorithm is proposed as a computational tool for solving the thin-lens structure of a triplet which consists of a singlet and an air-spaced doublet. The triplet is required to yield specified amounts of lens power and four primary aberrations: spherical aberration, coma, longitudinal chromatic aberration and secondary spectrum. In addition, the air spacing is used to control the zonal spherical aberration and spherochromatism. The problem is solved in the following manner. First, the equations for power and chromatic aberration are combined into a quartic polynomial equation if the object is at a finite distance, or combined into a quadratic polynomial equation if the object is at infinity. The roots give the element powers. Second, the lens shapes are obtained by solving the quartic polynomial equation which is obtained by combining the equations of spherical aberration and coma. Since quartic and quadratic equations can be solved using simple algebraic methods, the algor...

First-order analysis of a three-lens afocal zoom system

A general analysis for the first-order design of a three-lens afocal zoom system with one lens fixed is presented. The reasonable solution areas in the focal length diagrams with positive or negative mag- nification are derived and shown graphically. The relation between the two separations of the three lenses in zooming is found to be a hyper- bola. According to the different locations of hyperbola centers, four cases are analyzed. From the four hyperbolic graphs, we get five different types of zoom systems. For each zoom type, we find the maximum range of magnification and the position where the maximum or minimum system length occurs during zooming. The zoom loci for the first or sec- ond lens fixed are also discussed.

Design and fabrication of the diffractive phase element that synthesizes three-color pseudo-nondiffracting beams

National Chiao-Tung UniversityInstitute of Electro-Optical Engineering1001 Ta-Hsueh Road, Hsin-Chu 300Taiwan, Republic of China (ROC).E-mail: sze.eo88g@nctu.edu.twAbstract. The experimental implementation of the diffractive phase el-ement (DPE) that synthesizes three-color psudo-nondiffracting beams(PNDBs) is described. This DPE is designed with the amplitude-phaseretrieval method and fabricated by using optical contact lithography andreactive-ion etching (RIE). Measurements demonstrate that the fabri-cated DPE has the desired function, i.e., it forms a six-segment PNDBover a finite axial region and is monochromatic in each segment.

SOLUTION FOR FIRST-ORDER DESIGN OF A TWO-CONJUGATE ZOOM SYSTEM

The first-order solution is analyzed with particularly initial con- ditions for a two-conjugate zoom system that consists of three lenses. We find the solution ranges of system parameters with the conditions in which the object/image and pupil magnifications of the middle lens are taken to be 1 and 2 1o r 21 and 1, and the system magnification is 1 or 21 at the mean position of zooming. Several examples are given to demonstrate this analysis.

Analysis of the focal characteristics of cylindrical lenses made of anisotropically dielectric material based on rigorous electromagnetic theory

Abstract The focal characteristics of refractive cylindrical lenses made of anisotropically dielectric material (uniaxial crystal) are analysed based on rigorous electromagnetic theory and the boundary element method. The performances of the lenses with different f numbers are appraised for both incident waves of the TE (transverse electric) and TM (transverse magnetic) polarizations. Numerical results show that the focal performance of this kind of lens for the TE polarization and the TM polarization of incident light wave is a difference, in particular, different focal lengths, owing to the anisotropy of the material. However, for the conventional isotropic lens, the focal features for both the TE and TM polarizations are the same. It is anticipated that this new kind of lens proposed for the first time may serve as a light switching device with high speed used in the micro-optical communication.

Novel method to stabilize a laser wavelength unaffected by Fabry-Perot etalon angle drift

A laser with its wavelength stabilized to a Fabry-Perot etalon has many industrial applications. An ideal error signal for laser stabiliza- tion is the dispersion-like signal generated without wavelength modula- tion. We present a technique, by which the error signal is generated by the difference of two resonance peaks of a Fabry-Perot etalon. A laser beam is split into two beams, which pass through an etalon with a small optical path length difference to generate two partially overlapped reso- nance peaks. Subtracting one peak from the other yields a dispersion- like error signal. The zero crossing of the differential signal is insensitive to the angle drift of the etalon if the incident angles of the two laser beams are nearly equal but with opposite sign.