Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Collimation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Achromatic shearing phase sensor for generating images indicative of measure(s) of alignment between segments of a segmented telescope's mirrors

An achromatic shearing phase sensor generates an image indicative of at least one measure of alignment between two segments of a segmented telescope's mirrors. An optical grating receives at least a portion of irradiance originating at the segmented telescope in the form of a collimated beam and the collimated beam into a plurality of diffraction orders. Focusing optics separate and focus the diffraction orders. Filtering optics then filter the diffraction orders to generate a resultant set of diffraction orders that are modified. Imaging optics combine portions of the resultant set of diffraction orders to generate an interference pattern that is ultimately imaged by an imager.

Stahl, H. Philip↗
NASA NTRS1990

Real-time optical multiple object recognition and tracking system and method

System for optically recognizing and tracking a plurality of objects within a field of vision. Laser (46) produces a coherent beam (48). Beam splitter (24) splits the beam into object (26) and reference (28) beams. Beam expanders (50) and collimators (52) transform the beams (26, 28) into coherent collimated light beams (26', 28'). A two-dimensional SLM (54), disposed in the object beam (26'), modulates the object beam with optical information as a function of signals from a first camera (16) which develops X and Y signals reflecting the contents of its field of vision. A hololens (38), positioned in the object beam (26') subsequent to the modulator (54), focuses the object beam at a plurality of focal points (42). A planar transparency-forming film (32), disposed with the focal points on an exposable surface, forms a multiple position interference filter (62) upon exposure of the surface and development processing of the film (32). A reflector (53) directing the reference beam (28') onto the film (32), exposes the surface, with images focused by the hololens (38), to form interference patterns on the surface. There is apparatus (16', 64) for sensing and indicating light passage through respective ones of the positions of the filter (62), whereby recognition of objects corresponding to respective ones of the positions of the filter (62) is affected. For tracking, apparatus (64) focuses light passing through the filter (62) onto a matrix of CCD's in a second camera (16') to form a two-dimensional display of the recognized objects.

Chao, Tien-Hsin↗
NASA NTRS2006

Holographic memory using beam steering

A method, apparatus, and system provide the ability for storing holograms at high speed. A single laser diode emits a collimated laser beam to both write to and read from a photorefractice crystal. One or more liquid crystal beam steering spatial light modulators (BSSLMs) or Micro-Electro-Mechanical Systems (MEMS) mirrors steer a reference beam, split from the collimated laser beam, at high speed to the photorefractive crystal.

Chao, Tien-Hsin↗
NASA NTRS2007

Holographic memory using beam steering

A method, apparatus, and system provide the ability for storing holograms at high speed. A single laser diode emits a collimated laser beam to both write to and read from a photorefractice crystal. One or more liquid crystal beam steering spatial light modulators (BSSLMs) steer a reference beam, split from the collimated laser beam, at high speed to the photorefractive crystal.

Chao, Tien-Hsin↗
NASA NTRS2004

Stardust Encounters Comet 81P/Wild 2

Stardust successfully encountered comet 81P/Wild 2 on 2 January 2004 at a distance of 236.4 +/- 1 km. All encounter investigations acquired valuable new and surprising findings. The time-of-flight spectrometer registered 29 spectra during flyby and measured the first negative ion mass spectra of cometary particles. The dust detectors recorded particles over a broad mass range, 10(exp -11) to 10(exp -4) g. Unexpectedly, the dust distribution along Stardust's flight path was far from uniform, but instead occurred in short 'bursts', suggesting in-flight breakup of fragments ejected from the nucleus. High-resolution, stunning images of the Wild 2 surface show a diverse and complex variety of landforms not seen from comets 1P/Halley and 19P/Borrelly or icy satellites of the outer solar system. Longer-exposure images reveal large numbers of jets projected nearly around the entire perimeter of the nucleus, many of which appear to be highly collimated. A triaxial ellipsoidal fit of the Wild 2 nucleus images yields the principal nucleus radii of 1.65 X 2.00 X2.75 km (+/- 0.05 km). The orientations and source locations on the nucleus surface of 20 highly collimated and partially overlapping jets have been traced. There is every indication that the expected samples were successfully collected from the Wild 2 coma and are poised for a return to Earth on 15 January 2006.

Stardust mission↗
NASA NTRS2004

Models for the Infrared Cavity of HH 46/47

We have modeled the limb-brightened cavity seen in the new Spitzer Space Telescope IR images of the southwest lobe of HH 46/47 as the bow shock driven by an outflow from a young, low-mass star. We present models in which the outflow is a perfectly collimated, straight jet, models in which the jet precesses, and finally a model in which the outflow takes the form of a latitude-dependent wind. We study cases in which the outflow moves into a constant-density cloud and into a stratified cloud. We find that the best agreement with the observed cavity is obtained for the precessing jet in a stratified cloud. However, the straight jet (traveling in a stratified cloud) also gives cavity shapes close to the observed one. The latitude-dependent wind model that we have computed gives cavity shapes that are substantially wider than the observed cavity. We therefore conclude that the cavity seen in the Spitzer observations of the southwest lobe of the HH 46/47 outflow do not seem to imply the presence of a latitude-dependent wind, as it can be modeled successfully with a perfectly collimated jet model.

Herbig Haro objects↗
NASA NTRS2009

Particle-Image Velocimeter Having Large Depth of Field

An instrument that functions mainly as a particle-image velocimeter provides data on the sizes and velocities of flying opaque particles. The instrument is being developed as a means of characterizing fluxes of wind-borne dust particles in the Martian atmosphere. The instrument could also adapted to terrestrial use in measuring sizes and velocities of opaque particles carried by natural winds and industrial gases. Examples of potential terrestrial applications include monitoring of airborne industrial pollutants and airborne particles in mine shafts. The design of this instrument reflects an observation, made in field research, that airborne dust particles derived from soil and rock are opaque enough to be observable by use of bright field illumination with high contrast for highly accurate measurements of sizes and shapes. The instrument includes a source of collimated light coupled to an afocal beam expander and an imaging array of photodetectors. When dust particles travel through the collimated beam, they cast shadows. The shadows are magnified by the beam expander and relayed to the array of photodetectors. Inasmuch as the images captured by the array are of dust-particle shadows rather of the particles themselves, the depth of field of the instrument can be large: the instrument has a depth of field of about 11 mm, which is larger than the depths of field of prior particle-image velocimeters. The instrument can resolve, and measure the sizes and velocities of, particles having sizes in the approximate range of 1 to 300 m. For slowly moving particles, data from two image frames are used to calculate velocities. For rapidly moving particles, image smear lengths from a single frame are used in conjunction with particle- size measurement data to determine velocities.

Bos, Brent↗
NASA NTRS2009

Improved Scanners for Microscopic Hyperspectral Imaging

Improved scanners to be incorporated into hyperspectral microscope-based imaging systems have been invented. Heretofore, in microscopic imaging, including spectral imaging, it has been customary to either move the specimen relative to the optical assembly that includes the microscope or else move the entire assembly relative to the specimen. It becomes extremely difficult to control such scanning when submicron translation increments are required, because the high magnification of the microscope enlarges all movements in the specimen image on the focal plane. To overcome this difficulty, in a system based on this invention, no attempt would be made to move either the specimen or the optical assembly. Instead, an objective lens would be moved within the assembly so as to cause translation of the image at the focal plane: the effect would be equivalent to scanning in the focal plane. The upper part of the figure depicts a generic proposed microscope-based hyperspectral imaging system incorporating the invention. The optical assembly of this system would include an objective lens (normally, a microscope objective lens) and a charge-coupled-device (CCD) camera. The objective lens would be mounted on a servomotor-driven translation stage, which would be capable of moving the lens in precisely controlled increments, relative to the camera, parallel to the focal-plane scan axis. The output of the CCD camera would be digitized and fed to a frame grabber in a computer. The computer would store the frame-grabber output for subsequent viewing and/or processing of images. The computer would contain a position-control interface board, through which it would control the servomotor. There are several versions of the invention. An essential feature common to all versions is that the stationary optical subassembly containing the camera would also contain a spatial window, at the focal plane of the objective lens, that would pass only a selected portion of the image. In one version, the window would be a slit, the CCD would contain a one-dimensional array of pixels, and the objective lens would be moved along an axis perpendicular to the slit to spatially scan the image of the specimen in pushbroom fashion. The image built up by scanning in this case would be an ordinary (non-spectral) image. In another version, the optics of which are depicted in the lower part of the figure, the spatial window would be a slit, the CCD would contain a two-dimensional array of pixels, the slit image would be refocused onto the CCD by a relay-lens pair consisting of a collimating and a focusing lens, and a prism-gratingprism optical spectrometer would be placed between the collimating and focusing lenses. Consequently, the image on the CCD would be spatially resolved along the slit axis and spectrally resolved along the axis perpendicular to the slit. As in the first-mentioned version, the objective lens would be moved along an axis perpendicular to the slit to spatially scan the image of the specimen in pushbroom fashion.

Mao, Chengye↗
NASA NTRS2009

Critical Coupling Between Optical Fibers and WGM Resonators

Two recipes for ensuring critical coupling between a single-mode optical fiber and a whispering-gallery-mode (WGM) optical resonator have been devised. The recipes provide for phase matching and aperture matching, both of which are necessary for efficient coupling. There is also a provision for suppressing intermodal coupling, which is detrimental because it drains energy from desired modes into undesired ones. According to one recipe, the tip of the single-mode optical fiber is either tapered in diameter or tapered in effective diameter by virtue of being cleaved at an oblique angle. The effective index of refraction and the phase velocity at a given position along the taper depend on the diameter (or effective diameter) and the index of refraction of the bulk fiber material. As the diameter (or effective diameter) decreases with decreasing distance from the tip, the effective index of refraction also decreases. Critical coupling and phase matching can be achieved by placing the optical fiber and the resonator in contact at the proper point along the taper. This recipe is subject to the limitation that the attainable effective index of refraction lies between the indices of refraction of the bulk fiber material and the atmosphere or vacuum to which the resonator and fiber are exposed. The other recipe involves a refinement of the previously developed technique of prism coupling, in which the light beam from the optical fiber is collimated and focused onto one surface of a prism that has an index of refraction greater than that of the resonator. Another surface of the prism is placed in contact with the resonator. The various components are arranged so that the collimated beam is focused at the prism/resonator contact spot. The recipe includes the following additional provisions:

Matsko, Andrey↗
NASA NTRS2007

Compact Packaging of Photonic Millimeter-Wave Receiver

A carrier structure made from a single silicon substrate is the basis of a compact, lightweight, relatively inexpensive package that holds the main optical/electronic coupling components of a photonic millimeter-wave receiver based on a lithium niobate resonator disk. The design of the package is simple and provides for precise relative placement of optical components, eliminating the need for complex, bulky positioning mechanisms like those commonly used to align optical components to optimize focus and coupling. Although a prototype of the package was fabricated as a discrete unit, the design is amenable to integration of the package into a larger photonic and/or electronic receiver system. The components (see figure) include a lithium niobate optical resonator disk of 5-mm diameter and .200- m thickness, positioned adjacent to a millimeter- wave resonator electrode. Other components include input and output coupling prisms and input and output optical fibers tipped with ball lenses for focusing and collimation, respectively. Laser light is introduced via the input optical fiber and focused into the input coupling prism. The input coupling prism is positioned near (but not in contact with) the resonator disk so that by means of evanescent-wave coupling, the input laser light in the prism gives rise to laser light propagating circumferentially in guided modes in the resonator disk. Similarly, a portion of the circumferentially propagating optical power is extracted from the disk by evanescent-wave coupling from the disk to the output coupling prism, from whence the light passes through the collimating ball lens into the output optical fiber. The lens-tipped optical fibers must be positioned at a specified focal distance from the prisms. The optical fibers and the prisms must be correctly positioned relative to the resonator disk and must be oriented to obtain the angle of incidence (55 in the prototype) required for evanescent-wave coupling of light into and out of the desired guided modes in the resonator disk. To satisfy all these requirements, precise alignment features are formed in the silicon substrate by use of a conventional wet-etching process. These features include a 5-mm-diameter, 50- m-deep cavity that holds the disk; two trapezoidal-cross-section recesses for the prisms; and two grooves that hold the optical fibers at the correct positions and angles relative to the prisms and disk. The fiber grooves contain abrupt tapers, near the prisms, that serve as hard stops for positioning the lenses at the focal distance from the prisms. There are also two grooves for prismadjusting rods. The design provides a little slack in the prism recesses for adjusting the positions of the prisms by means of these rods to optimize the optical coupling.

Nguyen, Hung↗
NASA NTRS2006

Tunable-Bandwidth Filter System

A tunable-bandwidth filter system (TBFS), now undergoing development, is intended to be part of a remote-sensing multispectral imaging system that will operate in the visible and near infrared spectral region (wavelengths from 400 to 900 nm). Attributes of the TBFS include rapid tunability of the pass band over a wide wavelength range and high transmission efficiency. The TBFS is based on a unique integration of two pairs of broadband Raman reflection holographic filters with two rotating spherical lenses. In experiments, a prototype of the TBFS was shown to be capable of spectral sampling of images in the visible range over a 200-nm spectral range with a spectral resolution of .30 nm. The figure depicts the optical layout of a prototype of the TBFS as part of a laboratory multispectral imaging system for the spectral sampling of color test images in two orthogonal polarizations. Each pair of broadband Raman reflection holographic filters is mounted at an equatorial plane between two halves of a spherical lens. The two filters in each pair are characterized by steep spectral slopes (equivalently, narrow spectral edges), no ripple or side lobes in their pass bands, and a few nanometers of non-overlapping wavelength range between their pass bands. Each spherical lens and thus the filter pair within it is rotated in order to rapidly tune its pass band. The rotations of the lenses are effected by electronically controlled, programmable, high-precision rotation stages. The rotations are coordinated by electronic circuits operating under overall supervision of a personal computer in order to obtain the desired variation of the overall pass bands with time. Embedding the filters inside the spherical lenses increases the range of the hologram incidence angles, making it possible to continuously tune the pass and stop bands of the filters over a wider wavelength range. In addition, each spherical lens also serves as part of the imaging optics: The telephoto lens focuses incoming light to a field stop that is also a focal point of each spherical lens. A correcting lens in front of the field stop compensates for the spherical aberration of the spherical lenses. The front surface of each spherical lens collimates the light coming from the field stop. After the collimated light passes through the filter in the spherical lens, the rear surface of the lens focuses the light onto a charge-coupled-device image detector.

Aye, Tin↗
NASA NTRS2010

Instrument and method for X-ray diffraction, fluorescence, and crystal texture analysis without sample preparation

An X-ray diffraction and X-ray fluorescence instrument for analyzing samples having no sample preparation includes a X-ray source configured to output a collimated X-ray beam comprising a continuum spectrum of X-rays to a predetermined coordinate and a photon-counting X-ray imaging spectrometer disposed to receive X-rays output from an unprepared sample disposed at the predetermined coordinate upon exposure of the unprepared sample to the collimated X-ray beam. The X-ray source and the photon-counting X-ray imaging spectrometer are arranged in a reflection geometry relative to the predetermined coordinate.

Gendreau, Keith↗
NASA NTRS2011

Handbook of X-Ray Astronomy

X-ray astronomy was born in the aftermath of World War II as military rockets were repurposed to lift radiation detectors above the atmosphere for a few minutes at a time. These early flights detected and studied X-ray emission from the Solar corona. The first sources beyond the Solar System were detected during a rocket flight in 1962 by a team headed by Riccardo Giaccom at American Science and Engineering, a company founded by physicists from MIT. The rocket used Geiger counters with a system designed to reduce non-X-ray backgrounds and collimators limiting the region of sky seen by the counters. As the rocket spun, the field of view (FOV) happened to pass over what was later found to be the brightest non-Solar X-ray source; later designated See X-1. It also detected a uniform background glow which could not be resolved into individual sources. A follow-up campaign using X-ray detectors with better spatial resolution and optical telescopes identified See X-1 as an interacting binary with a compact (neutron star) primary. This success led to further suborbital rocket flights by a number of groups. More X-ray binaries were discovered, as well as X-ray emission from supernova remnants, the radio galaxies M87 and Cygnus-A, and the Coma cluster. Detectors were improved and Geiger counters were replaced by proportional counters, which provided information about energy spectra of the sources. A constant challenge was determining precise positions of sources as only collimators were available.

Arnaud, Keith A.↗
NASA NTRS2011

Receive Mode Analysis and Design of Microstrip Reflectarrays

Traditionally microstrip or printed reflectarrays are designed using the transmit mode technique. In this method, the size of each printed element is chosen so as to provide the required value of the reflection phase such that a collimated beam results along a given direction. The reflection phase of each printed element is approximated using an infinite array model. The infinite array model is an excellent engineering approximation for a large microstrip array since the size or orientation of elements exhibits a slow spatial variation. In this model, the reflection phase from a given printed element is approximated by that of an infinite array of elements of the same size and orientation when illuminated by a local plane wave. Thus the reflection phase is a function of the size (or orientation) of the element, the elevation and azimuth angles of incidence of a local plane wave, and polarization. Typically, one computes the reflection phase of the infinite array as a function of several parameters such as size/orientation, elevation and azimuth angles of incidence, and in some cases for vertical and horizontal polarization. The design requires the selection of the size/orientation of the printed element to realize the required phase by interpolating or curve fitting all the computed data. This is a substantially complicated problem, especially in applications requiring a computationally intensive commercial code to determine the reflection phase. In dual polarization applications requiring rectangular patches, one needs to determine the reflection phase as a function of five parameters (dimensions of the rectangular patch, elevation and azimuth angles of incidence, and polarization). This is an extremely complex problem. The new method employs the reciprocity principle and reaction concept, two well-known concepts in electromagnetics to derive the receive mode analysis and design techniques. In the "receive mode design" technique, the reflection phase is computed for a plane wave incident on the reflectarray from the direction of the beam peak. In antenna applications with a single collimated beam, this method is extremely simple since all printed elements see the same angles of incidence. Thus the number of parameters is reduced by two when compared to the transmit mode design. The reflection phase computation as a function of five parameters in the rectangular patch array discussed previously is reduced to a computational problem with three parameters in the receive mode. Furthermore, if the beam peak is in the broadside direction, the receive mode design is polarization independent and the reflection phase computation is a function of two parameters only. For a square patch array, it is a function of the size, one parameter only, thus making it extremely simple.

Rengarajan, Sembiam↗
NASA NTRS2006

Electronic Absolute Cartesian Autocollimator

An electronic absolute Cartesian autocollimator performs the same basic optical function as does a conventional all-optical or a conventional electronic autocollimator but differs in the nature of its optical target and the manner in which the position of the image of the target is measured. The term absolute in the name of this apparatus reflects the nature of the position measurement, which, unlike in a conventional electronic autocollimator, is based absolutely on the position of the image rather than on an assumed proportionality between the position and the levels of processed analog electronic signals. The term Cartesian in the name of this apparatus reflects the nature of its optical target. Figure 1 depicts the electronic functional blocks of an electronic absolute Cartesian autocollimator along with its basic optical layout, which is the same as that of a conventional autocollimator. Referring first to the optical layout and functions only, this or any autocollimator is used to measure the compound angular deviation of a flat datum mirror with respect to the optical axis of the autocollimator itself. The optical components include an illuminated target, a beam splitter, an objective or collimating lens, and a viewer or detector (described in more detail below) at a viewing plane. The target and the viewing planes are focal planes of the lens. Target light reflected by the datum mirror is imaged on the viewing plane at unit magnification by the collimating lens. If the normal to the datum mirror is parallel to the optical axis of the autocollimator, then the target image is centered on the viewing plane. Any angular deviation of the normal from the optical axis manifests itself as a lateral displacement of the target image from the center. The magnitude of the displacement is proportional to the focal length and to the magnitude (assumed to be small) of the angular deviation. The direction of the displacement is perpendicular to the axis about which the mirror is slightly tilted. Hence, one can determine the amount and direction of tilt from the coordinates of the target image on the viewing plane.

Leviton, Douglas B.↗
NASA NTRS2005

Laser Metrology for an Optical-Path-Length Modulator

Laser gauges have been developed to satisfy requirements specific to monitoring the amplitude of the motion of an optical-path-length modulator that is part of an astronomical interferometer. The modulator includes a corner-cube retroreflector driven by an electromagnetic actuator. During operation of the astronomical interferometer, the electromagnet is excited to produce linear reciprocating motion of the corner-cube retroreflector at an amplitude of 2 to 4 mm at a frequency of 250, 750, or 1,250 Hz. Attached to the corner-cube retroreflector is a small pick-off mirror. To suppress vibrations, a counterweight having a mass equal to that of the corner-cube retroreflector and pick-off mirror is mounted on another electromagnetic actuator that is excited in opposite phase. Each gauge is required to measure the amplitude of the motion of the pick-off mirror, assuming that the motions of the pick-off mirror and the corner-cube retroreflector are identical, so as to measure the amplitude of motion of the corner- cube retroreflector to within an error of the order of picometers at each excitation frequency. Each gauge is a polarization-insensitive heterodyne interferometer that includes matched collimators, beam separators, and photodiodes (see figure). The light needed for operation of the gauge comprises two pairs of laser beams, the beams in each pair being separated by a beat frequency of 80 kHz. The laser beams are generated by an apparatus, denoted the heterodyne plate, that includes stabilized helium-neon lasers, acousto-optical modulators, and associated optical and electronic subsystems. The laser beams are coupled from the heterodyne plate to the collimators via optical fibers.

Gursel, Yekta↗
NASA NTRS2004

Fresnel Lenses for Wide-Aperture Optical Receivers

Wide-aperture receivers for freespace optical communication systems would utilize Fresnel lenses instead of conventional telescope lenses, according to a proposal. Fresnel lenses weigh and cost much less than conventional lenses having equal aperture widths. Plastic Fresnel lenses are commercially available in diameters up to 5 m large enough to satisfy requirements for aperture widths of the order of meters for collecting sufficient light in typical long-distance free-space optical communication systems. Fresnel lenses are not yet suitable for high-quality diffraction-limited imaging, especially in polychromatic light. However, optical communication systems utilize monochromatic light, and there is no requirement for high-quality imaging; instead, the basic requirement for an optical receiver is to collect the incoming monochromatic light over a wide aperture and concentrate the light onto a photodetector. Because of lens aberrations and diffraction, the light passing through any lens is focused to a blur circle rather than to a point. Calculations for some representative cases of wide-aperture non-diffraction-limited Fresnel lenses have shown that it should be possible to attain blur-circle diameters of less than 2 mm. Preferably, the blur-circle diameter should match the width of the photodetector. For most high-bandwidth communication applications, the required photodetector diameters would be about 1 mm. In a less-preferable case in which the blur circle was wider than a single photodetector, it would be possible to occupy the blur circle with an array of photodetectors. As an alternative to using a single large Fresnel lens, one could use an array of somewhat smaller lenses to synthesize the equivalent aperture area. Such a configuration might be preferable in a case in which a single Fresnel lens of the requisite large size would be impractical to manufacture, and the blur circle could not be made small enough. For example one could construct a square array of four 5-m-diameter Fresnel lenses to obtain the same light-collecting area as that of a single 10-m-diameter lens. In that case (see figure), the light collected by each Fresnel lens could be collimated, the collimated beams from the four Fresnel lenses could be reflected onto a common offaxis paraboloidal reflector, and the paraboloidal reflector would focus the four beams onto a single photodetector. Alternatively, detected signal from each detector behind each lens would be digitized before summing the signals.

Hemmati, Hamid↗
NASA NTRS2003

Aligning Three Off-Axis Mirrors with Help of a DOE

A proposed method based on the use of a special-purpose diffractive optical element (DOE) would simplify (relative to prior methods) the alignment of three off-axis mirrors that constitute an imaging optical system. The method would exploit the fact that a DOE can be fabricated lithographically with high accuracy by electron-beam lithography in a thin film of poly(methyl methacrylate). The method would effectively transfer much of the problem of obtaining the needed accuracy from the mechanical-mirror-alignment domain to the lithographic domain. Unlike other methods that depend on specific symmetries (e.g., sphericity and/or concentricity), this method is expected to apply with equal ease and accuracy to mirrors of any configuration including aspherical, decentered mirrors. Assuming that one of the mirrors of a general three-mirror imaging optical system can serve as a reference for the alignment of the other two mirrors, such a system has 12 degrees of freedom in alignment. In the proposed method, one would use an interferometer in combination with a DOE to effect precise and relatively rapid and easy alignment of two of the mirrors with respect to each other, thus reducing the alignment task to that of the six degrees of freedom of the remaining mirror. The figure depicts a representative three-mirror off-axis imaging system, wherein the primary and tertiary mirrors (M1 and M3, respectively) are concave and the secondary mirror (M2) is convex. The DOE for aligning this system would be fabricated on the right surface of an optical flat and could be made to have either negative or positive focusing power, depending on the requirements of the specific application. The DOE could be designed to be placed at any convenient distance from M1 and M3 - again, depending on the application. The DOE would be illuminated with light coming from the left, generated by an interferometer. First, assuming the optical flat is of high quality, the plane of the DOE would be aligned perpendicular to the collimated beam by use of light reflected from the left face of the optical flat. The DOE would comprise two independent areas: one dedicated to M1, the other to M3. The portions of the collimated beam passing through those areas would be diffracted towards the corresponding mirrors. A mask, not shown in the figure, could be used to prevent light from passing through the rest of the area of the optical flat. Light rays reflected from M1 and M3 would retrace their paths through the DOE and would propagate leftward to the interferometer.

Mouroulis, Pantazis↗