A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Recent progress in flapping wing aerodynamics and aeroelasticity

Proceedings of SPIE - The International Society for Optical Engineering

More than a million insects and approximately 11,000 vertebrates utilize flapping wings to fly. However, flapping flight has only been studied in a few of these species, so many challenges remain in understanding this form of locomotion. Five key aerodynamic mechanisms have been identified for insect flight. Among these is the leading edge vortex, which is a convergent solution to avoid stall for insects, bats and birds. The roles of the other mechanisms - added mass, clap and fling, rotational circulation and wing-wake interactions - have not yet been thoroughly studied in the context of vertebrate flight. Further challenges to understanding bat and bird flight are posed by the complex, dynamic wing morphologies of these species and the more turbulent airflow generated by their wings compared with that observed during insect flight. Nevertheless, three dimensionless numbers that combine key flow, morphological and kinematic parameters - the Reynolds number, Rossby number and advance ratio - govern flapping wing aerodynamics for both insects and vertebrates. These numbers can thus be used to organize an integrative framework for studying and comparing animal flapping flight. Here, we provide a roadmap for developing such a framework, highlighting the aerodynamic mechanisms that remain to be quantified and compared across species. Ultimately, incorporating complex flight maneuvers, environmental effects and developmental stages into this framework will also be essential to advancing our understanding of the biomechanics, movement ecology and evolution of animal flight.

/pdf/flapping-wing-aerodynamics-from-insects-to-vertebrates-1khyr2udnj.pdf

Flapping wing aerodynamics: from insects to vertebrates

A fluid-structure interaction model of insect flight with flexible wings

This work demonstrates techniques that advance the standard practice in spindle metrology and enable five degree-of-freedom calibration of precision spindles with nanometer-level error motion. Several improvements are described in this paper: (1) an improved implementation of Donaldson and Estler reversal that eliminates moving and realigning the displacement sensor, (2) frequency domain low-pass filtering of data to remove spectral content without distortion, (3) robust removal of low frequency components caused by thermal drift and fluctuations in air bearing supply pressure, and (4) three-dimensional display of the synchronous error motion in the radial and axial directions. Example measurements demonstrate the repeatability and reproducibility of the techniques. Furthermore, synchronous radial error motion of an air bearing spindle calibrated by multi-step, master artifact, and master axis techniques agree within 1 nm.

/pdf/techniques-for-calibrating-spindles-with-nanometer-error-2gpvcrulpo.pdf

Techniques for calibrating spindles with nanometer error motion

This work demonstrates the state of the art capabilities of three error separation techniques for nanometer-level measurement of precision spindles and rotationally-symmetric artifacts. Donaldson reversal is compared to a multi-probe and a multi-step technique using a series of measurements carried out on a precision aerostatic spindle with a lapped spherical artifact. The results indicate that subnanometer features in both spindle error motion and artifact form are reliably resolved by all three techniques. Furthermore, the numerical error values agree to better than one nanometer. The paper discusses several issues that must be considered when planning spindle or artifact measurements at the nanometer level.

/pdf/nanometer-level-comparison-of-three-spindle-error-motion-jl5fx891hn.pdf

Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques

Insects produce thrust and lift forces via coupled fluid–structure interactions that bend and twist their compliant wings during flapping cycles. Insight into this fluid–structure interaction is achieved with numerical modeling techniques such as coupled finite element analysis and computational fluid dynamics, but these methods require accurate and validated structural models of insect wings. Structural models of insect wings depend principally on the shape, dimensions and material properties of the veins and membrane cells. This paper describes a method for parametric modeling of wing geometry using digital images and demonstrates the use of the geometric models in constructing three-dimensional finite element (FE) models and simple reduced-order models. The FE models are more complete and accurate than previously reported models since they accurately represent the topology of the vein network, as well as the shape and dimensions of the veins and membrane cells. The methods are demonstrated by developing a parametric structural model of a cicada forewing.

http://iopscience.iop.org/article/10.1088/1748-3182/4/3/036004/pdf

Parametric structural modeling of insect wings.

An integrated program of research aimed at understanding wing flexibility and its implications for flight in insects is described. The experimental component of the research involves quantitative, high-speed videogrammetry of insects in free flight along with measurements of the mass and structural properties of the insect body and wings. The computational component of the research is centered on high-fidelity, flow and flowstructure interaction (FSI) modeling of insects in flight. The experiments provide data for the parameterization as well as the validation of the computational models.

A combined experimental-numerical study of the role of wing flexibility in insect flight

This technical note examines an approach to measuring the roundness of spherical artifacts at arbitrary latitude. A roundness measurement includes the combined contributions from the artifact’ form error and the spindle’ error motion. We show that it is possible to separate the spindle error from artifact form error at any inclination with respect to the axis of rotation if the axial and radial error motion is independently measured using an error separation technique such as Donaldson reversal. Comparison of the predicted and measured results shows agreement to less than a nanometer.

/pdf/roundness-measurement-of-spherical-artifacts-at-arbitrary-rkd4dg5bbr.pdf

Ryan Vallance

Papers

Techniques for calibrating spindles with nanometer error motion

Nanometer-Level Comparison of Three Spindle Error Motion Separation Techniques

Parametric structural modeling of insect wings.

A combined experimental-numerical study of the role of wing flexibility in insect flight

Roundness measurement of spherical artifacts at arbitrary latitude