Development of a three-degree-of-freedom piezoelectric actuator.

Multi-degree of freedom piezoelectric actuators are strongly needed for industrial applications, especially when manipulating a large and heavy mirror or lens in an optical system. A novel three-degree-of-freedom piezoelectric actuator, which is driven by two pairs of piezo-stack actuator with spatial compliant mechanisms designed to guide the motion and preload the piezo-stack actuators, is herein proposed. The structure and working principle of the proposed actuator are illustrated and its kinematic characteristic is analyzed. The stiffness of the spatial compliant mechanisms is modeled, and the dynamic characteristics are analyzed, Finite Element method is utilized to validate the correctness of the stiffness modeling and the free vibration analysis of the proposed actuator. A prototype actuator is fabricated and its output performances have been tested. Working space of X ranging from -7.1 to 5.6 µm, Y ranging from -6.2 to 8.2 µm and Z ranging from -2.3 to 2.1 µm, displacement resolutions of 15/16/21 nm along X-/Y-/Z-axis and average velocities of 52.3, 82.8 and 29.5 µm/s along X-axis, Y-axis, and Z-axis with carrying load up to 2 kg and driving frequency of 500 Hz have been achieved by the prototype actuator. The method of waveform generating for the proposed actuator has been developed with the inverse hysteresis compensation, and test results indicate that the positioning accuracy of the prototype actuator in the open loop has been improved from 0.94 to 0.23 µm for a circular trajectory tracking, from 0.48 to 0.29 µmm for an elliptical trajectory tracking, and from 0.61 to 0.32 µm for a rectangular trajectory tracking with the compensated waveform of driving voltage.

A New Stitching Method for Dark-Field Surface Defects Inspection Based on Simplified Target-Tracking and Path Correction.

A camera-based dark-field imaging system can effectively detect defects of microns on large optics by scanning and stitching sub-apertures with a small field of view. However, conventional stitching methods encounter problems of mismatches and location deviations, since few defects exist on the tested fine surface. In this paper, a highly efficient stitching method is proposed, based on a simplified target-tracking and adaptive scanning path correction. By increasing the number of sub-apertures and switching to camera perspective, the defects can be regarded as moving targets. A target-tracking procedure is firstly performed to obtain the marked targets. Then, the scanning path is corrected by minimizing the sum of deviations. The final stitching results are updated by re-using the target-tracking method. An experiment was carried out on an inspection of our specially designed testing sample. Subsequently, 118 defects were identified out of 120 truly existing defects, without stitching mismatches. The experiment results show that this method can help to reduce mismatches and location deviations of defects, and it was also effective in increasing the detectability for weak defects.

Design and engineering verification of an ultrashort throw ratio projection system with a freeform mirror.

A refractive-reflective combined ultrashort throw ratio projection optical system is designed. We use a freeform mirror to shorten the projection distance and correct distortion, and a plane mirror to turn back the optical path and reduce system volume. The projection system design method combines refractive lens group design and freeform surface mirror design with integrated optimization. The system's throw ratio is 0.11 with a projection distance of 320 mm and a 130 in. (1 in.=25.4 mm) screen size, which illustrates the advantages of the low throw ratio. The system's maximum distortion is 0.07%. To demonstrate the proposed system's performance, a prototype is developed. Experimental results confirm that the system performs excellently while meeting the design requirements. The system's advantages include low throw ratio, excellent imaging quality, miniaturization, and engineering feasibility.

Adaptive Spiral Tool Path Generation for Diamond Turning of Large Aperture Freeform Optics.

Slow tool servo (STS) diamond turning is a well-developed technique for freeform optics machining. Due to low machining efficiency, fluctuations in side-feeding motion and redundant control points for large aperture optics, this paper reports a novel adaptive tool path generation (ATPG) for STS diamond turning. In ATPG, the sampling intervals both in feeding and cutting direction are independently controlled according to interpolation error and cutting residual tolerance. A smooth curve is approximated to the side-feeding motion for reducing the fluctuations in feeding direction. Comparison of surface generation of typical freeform surfaces with ATPG and commercial software DiffSys is conducted both theoretically and experimentally. The result demonstrates that the ATPG can effectively reduce the volume of control points, decrease the vibration of side-feeding motion and improve machining efficiency while surface quality is well maintained for large aperture freeform optics.

High-performance laser projection display illumination system based on a diffractive optical element.

Lasers have been regarded as the potential illumination source for next generation projectors. With the additional feature of coherency, diffractive optical elements (DOEs) become available in the illumination light path. DOEs in laser projection display systems add strong beam-shaping ability, good uniform performance and small size, which makes it is possible to realize efficient and uniform illumination on a spatial light modulator (SLM). Moreover, it is helpful for the simplification and compactness of illumination optics. This paper proposed what we believe is a novel RGB laser projection display illumination system based on a DOE, which used the DOE and optical path compensation system (OPCS) as the beam-shaping and relay system (BSRS), instead of a light pipe and relay lens group in the conventional laser projection display illumination system. We designed the DOE and established the simulation model of the illumination system. The simulation results show that the new illumination system is simple and compact, the illumination uniformity is more than 90%, the illumination efficiency of RGB illumination in BSRS is more than 75%, and the numerical aperture (NA) of the illumination beam is about 0.01.

Piezoelectric Actuated Phase Shifter Based on External Laser Interferometer: Design, Control and Experimental Validation.

To improve the phase-shifting accuracy, this paper presents a novel integrated framework for design, control and experimental validation of the piezoelectric actuated phase shifter with a trade-off between accuracy and cost. The piezoelectric actuators with built-in sensors are adopted to drive the double parallel four-bar linkage flexure hinge-based mechanisms. Three mechanisms form the tripod structure of the assembled phase shifter. Then, a semi-closed loop controller with inner feedback and outer feedforward loops via the external laser interferometer is developed for accurate positioning of the phase shifter. Finally, experiments related with travel range, step response, linearity and repeatability are carried out. The linearity error is 0.21% and the repeatability error of 10 µ m displacement is 3 nm. The results clearly demonstrate the good performance of the developed phase shifter and the feasibility of the proposed integrated framework.

Analysis and experiments of the thermal-optical performance for a kinematically mounted lens element.

In order to evaluate the thermal-optical performance of a kinematic mounting applied in lithographic projection lens, the optical surface figure and wavefront changes of the lens element under a certain thermal load are investigated with both experimental and numerical simulation methods. From the experimental and numerical results, the temperature on the edge of the lens element rises up to 22.51°C, and the center of lens is 5.3°C higher. As a result, this thermal nonuniformity leads to a 9.622 nm RMS change of the optical surface figure and 71.905 nm RMS change of the index inhomogeneity, consisting mainly of Z4, Z9, and Z16. Because of the radial flexibility of the supporting legs of the kinematic mounting, aberrations such as pri trefoil and sec trefoil are less than 2% of the total wavefront changes, and other nonaxisymmetric aberrations are negligible. The Zernike coefficient differences between experiments and simulation are less than 2 nm, which supports the correctness of our method. The kinematic mounting shows good thermal adaptability, and the method for evaluation of the thermal-optical characteristics is proved effective.

Absolute surface figure testing by shift-rotation method using Zernike polynomials.

In surface figure testing, most of them are relative tests, and the reference surface usually limits the accuracy of test results. Absolute calibration is one of the most important and efficient techniques to reach subnanometer accuracy in surface figure testing. An absolute testing method, a shift-rotation method using Zernike polynomials, is presented, which can be used to calibrate both flat and spherical surfaces (concave or convex). Calibration contains at least three position measurements: one basic position, one rotation, and one lateral shift of the test surface. Experiments show that the repeatability of this method is 0.13 nm RMS, and pixel-to-pixel comparison with the two-sphere method is 0.2 nm RMS.

Mathematical construction and perturbation analysis of Zernike discrete orthogonal points.

Zernike functions are orthogonal within the unit circle, but they are not over the discrete points such as CCD arrays or finite element grids. This will result in reconstruction errors for loss of orthogonality. By using roots of Legendre polynomials, a set of points within the unit circle can be constructed so that Zernike functions over the set are discretely orthogonal. Besides that, the location tolerances of the points are studied by perturbation analysis, and the requirements of the positioning precision are not very strict. Computer simulations show that this approach provides a very accurate wavefront reconstruction with the proposed sampling set.

A high-accuracy and convenient figure measurement system for large convex lens.

We present a novel optical configuration of a phase-shifting interferometer for high-accuracy figure metrology of large dioptric convex spherical surfaces. The conformation and design considerations according to measurement accuracy, practicability, and system errors analysis are described. More in detail, we show the design principle and methods for the crucial parts. Some are expounded upon with examples for thorough understanding. The measurement procedures and the alignment approaches are also described. Finally, a verification experiment is further presented to verify our theoretical design. This system gives full-aperture and high-precision surface testing while maintaining relatively low cost and convenient operation.

Design of algorithms for phase shifting interferometry using self-convolution of the rectangle window.

The objective of this paper is to design phase shifting algorithms error-resistant to the nonlinearity of phase-shift error and photoelectric detector simultaneously. An effective construction approach is proposed based on self-convolution of the rectangle window to design algorithms with perfect zero point distribution, according to the fact that the error-resistant capability is entirely determined by the number and order of zero points of Fourier transform of the related window function. Theoretical analysis and numerical simulations compared to the commercial 13-frame algorithm demonstrate the validity of the approach to design algorithms with enhanced error-resistant capability not only to CCD-caused harmonics but also to PZT ramping nonlinearity.

[Measurement technology for relative spectral responsivity of the ultraviolet ICCD].

The spectral responsivity is one of the important parameters of detector. With the development of ultraviolet detect technique accurate measure for the spectral responsivity of ultraviolet detector becomes more and more important. A measure principle which is based on the direct comparison measuring method for relative spectral response measurement of the ultraviolet ICCD is introduced. Based on the scientific-grade spectrometer with ultraviolet responsivity, a measurement facility was built. The relative spectral responsivity curve of the ultraviolet ICCD was obtained. The curve indicates that the spectral-response of UV-ICCD is from 220 to 300 nm and the peak response is near 270 nm, which indicates that the UV-ICCD is solar blind. The analysis of the uncertainty shows that the most largest uncertainty of measurement for relative spectral responsivity of the UV-ICCD is 7.79% and meets the requirement.