Low-stray-light gratings fabricated with scanning exposure method based on Lloyd's mirror for a high-contrast near-eye display in augmented reality.

The stray light of gratings lowers the image contrast of augmented reality display devices based on lightguide gratings. We propose to reduce the stray light of gratings fabricated with the scanning exposure method in a Lloyd's mirror interferometer setup. The photoresist-coated substrate is moved in the longitudinal direction parallel to the exposure interference fringes during exposure to average out the laser speckle-induced noise. A phase locking module is designed to compensate for the unwanted lateral displacement caused by the straightness error and vibration of the translation stage. The stability and accuracy of phase locking in the Lloyd's mirror interferometer are analyzed with control system theory. Low-stray-light lightguide gratings were fabricated successfully. The stray light level was decreased by more than 50%, and the imaging contrast was increased from 65% to 85%.

Blazed gratings with both controllable blaze angle and anti-blaze angle fabricated by using a twice oblique ion beam etching method.

A twice oblique ion beam etching method is proposed to fabricate triangular blazed gratings that have controllable both blaze angle and anti-blaze angle. The anti-blaze angle is controlled by first obliquely etching the photoresist mask to obtain an asymmetrical trapezoidal grating, one sidewall of which then evolves into the anti-blaze facet in the second etch step. The blaze angle is controlled by obliquely etching the asymmetrical trapezoidal grating to obtain a triangular blazed grating. We show the key process steps of the method by fabricating a blazed grating with the blaze angle of 20.9° and the anti-blaze angle of 89.0°. The method is verified not only to increase the anti-blaze angle to near 90°, but also have a good tolerance against over-etching.

Improved 2D continuously variable output couplers for an exit pupil expander fabricated through ion beam etching.

An important goal in designing a head-mounted display device is to improve its exit pupils' output light areal uniformity. The goal cannot be reached by using an output grating coupler of uniform surface profile depth. To solve this problem, we propose a method to fabricate 2D and continuously variable depth gratings by using a specially modified reactive ion-beam etching system, which features variable speed scanning etching and ion beam cross-sectional shaping in two orthogonal dimensions. We experimentally verified that the uniformity of the light outcoupled from the coupler fabricated by using the proposed method was 52% better than that of a uniform-depth output grating coupler.

Aberration-reduced spherical concave grating holographically recorded by a spherical wave and a toroidal wave for Rowland circle mounting.

We propose a new recording system that employs a spherical wave and a toroidal wave to holographically record an aberration-reduced Rowland-circle spherical grating. Two more variables in this recording system are available for the design compared with a conventional symmetric dual-plane-wave recording system, which allows both the astigmatism and sagittal coma of the grating to be corrected to minimum. We derive the aberration coefficients of such grating and give the universal design principles for the recording system. An aberration-reduced grating used in a spectrometer equipped with linear array CCDs is then specifically designed and fabricated. The performances of the aberration-reduced grating and that of the conventional grating recorded by dual plane waves are compared in terms of the ray-tracing spot diagrams, and the photographed spectral images. The experimental results show that the spectral intensity of the aberration-reduced grating is about 4.5 times that of the conventional grating, while the resolution of the aberration-reduced grating is close to that of the conventional grating.

Astigmatism-reduced spherical concave grating holographically recorded by a cylindrical wave and a plane wave for Rowland circle mounting.

We propose a new recording system that employs a cylindrical wave and a plane wave to holographically record astigmatism-reduced Rowland-circle spherical gratings. We find that the astigmatism of the grating can be sharply reduced, so that the spectral intensity is improved. Meanwhile, its defocus aberration and meridional coma remain zero throughout the working spectrum, meaning the spectral resolution is similar to that of a conventional grating recorded by symmetric dual plane waves. We designed and made one astigmatism-reduced grating and one conventional grating for an actual Rowland-circle spherical-grating spectrometer. Our experimental results showed that the spectral intensity of the astigmatism-reduced grating is about five times that of the conventional grating, while the resolution of the astigmatism-reduced grating is close to that of the conventional grating.

Achieving unlimited recording length in interference lithography via broad-beam scanning exposure with self-referencing alignment.

Large-area holographic gratings are of great importance in diverse fields including long-range interference metrology, high-resolution astronomical telescopes, and chirped-pulse-amplification systems. However, in conventional interference lithography, the recording length is limited by the aperture of the collimating lenses. Here we propose broad-beam scanning exposure which employs the latent grating generated continuously during scanning for real-time dynamic fringe locking and thus achieves unlimited recording length. This method is experimentally proved to make high-quality gratings, and is expected to be a new type of interference lithography.

Duty cycle estimate of photoresist gratings via monitoring TM/TE diffraction efficiency ratio during development.

We present an in situ duty cycle control method that relies on monitoring the TM/TE diffraction efficiency ratio of the -1st transmitted order during photoresist development. Owing to the anisotropic structure of a binary grating, at an appropriately chosen angle of incidence, diffraction efficiencies in TE and TM polarizations vary with groove depth proportionately, while they vary with duty cycle differently. Thus, measuring the TM/TE diffraction efficiency ratio can help estimate the duty cycle during development while eliminating the effect of photoresist thickness uncertainty. We experimentally verified the feasibility of this idea by fabricating photoresist gratings with different photoresist thicknesses. The experimental results were in good agreement with theoretical predictions.

Two-probe optical encoder for absolute positioning of precision stages by using an improved scale grating.

In this paper, a novel optical encoder enabling the simultaneous measurement of displacement and the position of precision stages is presented. The encoder is composed of an improved single-track scale grating and a compact two-probe reading head. In the scale grating, multiple reference codes are physically superimposed onto the incremental grooves, in contrast to conventional designs, where an additional track is necessary. The distribution of the reference codes follows a specific mathematical algorithm. For the reading head, a two-probe structure is designed to identify the discrete reference codes by means of the superimposition of the codes with a stationary mask and to read the continuous incremental grooves by means of a grating interferometry, respectively. A prototype encoder was designed, constructed and evaluated, and experimental results show that the distance code precision achieved is 0.5 µm, while the linearity error of the linear displacement measurement is less than 0.06%.

Controlling the duty cycle of holographic crossed gratings by in situ endpoint detection during development.

A method of in situ development endpoint detection is proposed to control the duty cycle of holographic crossed gratings. Based on the observation that after the developer first touches the substrate surface the topography of the crossed grating undergoes an evolution process from a hole array of increasing diameter to a pillar array of decreasing diameter, we set up a development model. In this model, the shapes of both holes and pillars are assumed to have square in-plane cross sections, rotated 45° with respect to the main periodic directions, and straight side walls perpendicular to the grating plane. Thus, the main development process, including the transition from a hole array to a pillar array, can be characterized by a single parameter continuously, and the change of diffraction efficiency during the process can be theoretically calculated. Two different in situ development monitoring conditions were simulated and tested experimentally. Using this method, crossed gratings with various duty cycles were fabricated under different incident and monitoring conditions.

Analysis and minimization of spacing error of holographic gratings recorded with spherical collimation lenses.

This research proposes a feedback method to adjust the dual-beam exposure system with spherical collimation lenses to achieve gratings with low spacing error. Through theoretical analysis and numerical calculation, it is proved that the interference aberration can be analyzed with the Zernike polynomials and the adjustment errors can be estimated according to the linear relationship between the errors and the polynomial coefficients. Moreover moving the substrate along its normal is proposed to decrease the spacing error but keep the grating's period unchanged. In the experiments, the wavefront measurement results of the ± 1st orders are used to deduce the spacing error. Based on the feedback adjustment method, the grating with a spacing error of 0.03 λ within 70 mm × 70 mm is fabricated with the collimation lenses of 0.6 λ spherical aberration.

Fabrication of low-stray-light gratings by broad-beam scanning exposure in the direction perpendicular to the grating grooves.

Previous research on making low-stray-light gratings is mainly focused on process steps after the photoresist mask has been made. We propose to improve the quality of the photoresist mask directly in exposure. We present a broad-beam scanning exposure method along the grating vector (i.e., in the direction perpendicular to the grating grooves), utilizing a reference grating clamped below the substrate on the translation stage for phase and attitude locking. Scanning-exposed gratings with a size of 40 mm×40 mm are successfully made, which have straighter grooves and smoother surfaces, and their stray light levels around the first and second diffraction orders are decreased significantly.

Scatterometry specialized for a highly asymmetric triangular grating on a transparent substrate.

We present a specialized scatterometry method to measure the groove profiles of highly asymmetric triangular gratings. Compared with the conventional scatterometry working in a specular way, this method utilizes diffraction spectra of the reflected ±1st orders and is good at measuring this kind of asymmetric grating with a higher sensitivity. In our work, diffraction efficiency angular spectra at a single wavelength are measured and passed on to a parameter optimization process to retrieve three profile defining parameters. Final results are compared with the ones from an atomic force microscope and discrepancies are discussed and explained.

Fabrication of optical mosaic gratings: a self-referencing alignment method.

We propose and demonstrate a self-referencing alignment technique to conveniently enlarge fabricated grating area. The latent image gratings are used as the reference objects to align (adjust and lock) the attitude and position of the substrate relative to the exposure beams between and during consecutive exposures. The adjustment system and the fringe-locking system are combined into the exposure system, eliminating the drift errors between them and making the whole system low-cost and compact. For the fabricated 1 × 4 mosaics of 50 × (30 + 30 + 30 + 30) mm(2) area and 1 × 2 mosaics of 90 × (80 + 80) mm(2) area, the typical peak-valley -1st-order wavefront errors measured by a 100-mm-diameter interferometer are not more than 0.06 λ and 0.09 λ, respectively.

Fabrication of optical mosaic gratings with phase and attitude adjustments employing latent fringes and a red-wavelength dual-beam interferometer.

We present a method to make optical mosaic gratings that uses the exposure beams and the latent grating created by the previous exposure to adjust the lateral position and readjust the attitude of the substrate for the current exposure. As thus, it is a direct method without using any auxiliary reference grating(s) and it avoids the asynchronous drifts between otherwise independent exposure and alignment optical sub-systems. In addition, the method uses a red laser wavelength in the plane-mirror interferometers for the multi-dimensional attitude adjustment, so the adjustment can be done at leisure. The mosaic procedure is described step by step, and the principles to minimize substrate alignment errors are explained in detail. Experimentally we made several mosaics of (50 + 30) x 50 mm(2) final grating area. The typical peak-valley and root-mean-square values of the measured -1st-order diffraction wavefront errors are 0.036 lambda and 0.006 lambda, respectively.

Measurement of period difference in grating pair based on compensation analysis of phase difference between diffraction beams.

We propose an experimental method for measuring the period difference in a grating pair. The method uses the relationship between the period difference and the phase difference of diffraction beams of the grating pair when gratings are translated along the grating-vector direction. The effect of the roll angular deviation of gratings can be eliminated by phase compensation with +1st- and -1st-order diffraction beams. Far-field intensity patterns of diffraction beams are monitored to adjust the relative attitude of gratings. For a pair of gratings with periods of approximately 0.674 microm, the period difference was measured to be 0.4434 nm with an expanded uncertainty (k=2) of 0.0113 nm.

[Numerical simulation and experimental demonstration of error compensation between recording structure and use structure of flat-field holographic concave gratings].

A flat-field holographic concave grating can be the only optical element in a spectrometer. If the mutually compensating roles of the concave grating and the spectrometer are taken into account, the difficulty of fabricating concave grating can be reduced. When the holographic method is used to make concave gratings, it is very difficult to fix precisely the spatial distances between the two recording points and the vertex of concave gratings. In like manner, it is also difficult to fix precisely the location of the entrance slit or the CCD in using concave gratings in spectrometers. In other words, during the fabrication stage and the end-use stage of concave gratings, there are inevitable errors between the practical system structure parameters and the theoretical ones. The authors name them fabrication structure errors and end-use structure errors, respectively. Numerical simulation indicates that these two classes of errors will seriously deteriorate the spectral image quality. At present, there are few references describing the elimination of the fabrication and end-use errors of concave gratings. In this paper, a concave grating used in a compact chromatograph is analyzed as an example. By performing numerical simulations that take both fabrication structure parameters and end-use structure parameters into consideration, we found that in a large neighborhood around the design point, the two sets of parameters can mutually compensate. This means that even both sets are away from the optimized design points, as long as proper compensations are made, the spectral image quality of the spectrometer can be as good as designed. In other words, on the one hand, for a specific concave grating that has been made with some fabrication structure errors, we can move the CCD to find an appropriate location where the spectral image quality is as good as designed; On the other hand, for a decided end-use system which has some end-use structure errors, we can adjust the fabrication structure to make concave gratings that will generate good spectral images in this end-use system. The experiment results show that this method is an effective way to adjust the optical system for grating fabrication. The authors also give experimental results that agree with simulation results. Such compensation can reduce both the alignment difficulty and the required precision of fabrication structure parameters of concave gratings. It could also give theoretical guidance to the design and assembly of spectrometers.

Routine turning maneuvers of koi carp Cyprinus carpio koi: effects of turning rate on kinematics and hydrodynamics.

Spontaneous swimming behaviors of koi carp Cyprinus carpio koi were recorded using a video tracking system. Routine single-beat turns were selected from the recorded image sequences for kinematic and hydrodynamic analysis. As with C-starts, the turns can be divided into two stages (stage 1 and stage 2), based on kinematics. Stage 1 involves a bend to one side forming a C-shaped curve in the body, while stage 2 corresponds to the return flip of the body and tail. The turning angle in stage 1 accounts for the greatest portion of the total turning angle and the mean turning rate in stage 1 reflects the intensity of turn. The effects of the turning rate in stage 1 on both kinematics and hydrodynamics were examined. The duration of stage 1 remained relatively stable over a nearly tenfold change in turning rate. Consequently, the turning angle is dominated by the turning rate in stage 1. The turning radius is not related to the swimming speed. Moreover, except in very fast turns, the turning radius is also not affected by the turning rate. The angle between the side jet and the carp's initial orientation of a turn does not change substantially with the turning rate, and it is always close to 90 degrees (94.2+/-3.1 degrees , N=41), so the orientation of the side jet in the forthcoming turn can be predicted. The angle between the jet and the line joining the center of mass of the carp and the trailing edge of the tail (mean value in stage 1) is also always close to 90 degrees (95.3+/-1.3 degrees , N=41). It is helpful for the carp to maximize the torque so as to improve the turning efficiency. In stage 1, the impulsive moment obtained from the beat of the body and tail and the mean angular momentum of the carp show an agreement in magnitude. Two types of flow patterns in the wake of routine single-beat turns are revealed. The difference between the two types of wakes is in whether or not a vortex ring and a thrust jet are generated in stage 2. The recoil speed of the tail, the bending amplitude of the turn, and the angle of attack of the tail are three probable factors influencing the flow patterns in stage 2.

Grating mosaic based on image processing of far-field diffraction intensity patterns in two wavelengths.

A practical grating mosaic method is proposed based on quantitative image processing of three far-field diffraction intensity patterns in two wavelengths. This method aims at making a perfect mosaic of two planar gratings that can substitute for a single and larger grating without introducing wavefront aberration at any wavelength. The zeroth-order and first-order far-field patterns of one wavelength are analyzed for separating and eliminating the angular mosaic errors. The first-order far-field patterns of two wavelengths are applied for separation of the lateral and longitudinal phase errors. Then the three patterns are considered together to enlarge the target range of coarse adjustment required for further fine adjustment in longitudinal position. Experimentally, angular and positional detection sensitivities of less than 6 microrad and 14 nm were achieved, respectively, and the periodicity in positional adjustment was checked, which departed less than 1.8% from the theoretical period. The performance of the perfect mosaic grating was diagnosed with the far-field diffraction intensity pattern in a third wavelength, and the necessity for a perfect mosaic was verified.

Kinematics, hydrodynamics and energetic advantages of burst-and-coast swimming of koi carps (Cyprinus carpio koi).

Koi carps frequently swim in burst-and-coast style, which consists of a burst phase and a coast phase. We quantify the swimming kinematics and the flow patterns generated by the carps in burst-and-coast swimming. In the burst phase, the carps burst in two modes: in the first, the tail beats for at least one cycle (multiple tail-beat mode); in the second, the tail beats for only a half-cycle (half tail-beat mode). The carp generates a vortex ring in each half-cycle beat. The vortex rings generated during bursting in multiple tail-beat mode form a linked chain, but only one vortex ring is generated in half tail-beat mode. The wake morphologies, such as momentum angle and jet angle, also show much difference between the two modes. In the burst phase, the kinematic data and the impulse obtained from the wake are linked to obtain the drag coefficient (C(d,burst) approximately 0.242). In the coast phase, drag coefficient (C(d,coast) approximately 0.060) is estimated from swimming speed deceleration. Our estimation suggests that nearly 45% of energy is saved when burst-and-coast swimming is used by the koi carps compared with steady swimming at the same mean speed.

Optical mosaic gratings made by consecutive, phase-interlocked, holographic exposures using diffraction from latent fringes.

We propose and demonstrate a method for fabricating large optical mosaic gratings, i.e., gratings made by consecutive, phase-interlocked, holographic exposures on single substrates. It takes advantage of the latent fringes generated by the preceding exposure to align the substrate for the following exposure. Good angular alignment accuracy and period consistency between the fringes recorded by consecutive exposures can be achieved by using the large-area moiré pattern produced by the latent fringes and the alignment beams. Phase-interlocking accuracy of less than 4 degrees between consecutive exposures was experimentally achieved by using the heterodyne detection technique.