Comparison of mechanically ruled versus holographically varied line-spacing gratings for a soft-x-ray flat-field spectrograph

Recent progress in the design of aspheric wave-front recording systems has permitted the manufacture of holographic gratings with highly variable groove densities that are suitable for flat-field spectrographs. A holographic grating thus recorded was processed to produce a laminar profile by use of reactive-ion etching. Measurements are reported of the absolute diffraction efficiency of this grating and of a comparable mechanically ruled grating. It is found that the holographic grating is much more effective in suppressing the higher orders. The spectral resolution was determined by use of a carbon Kalpha x-ray generator and a spectrograph with an imaging detector. The spectral resolution of the holographic grating was approximately 3 times worse than that of the ruled grating.     

Varied line spacing plane holographic grating recorded by using uniform line spacing plane gratings

Uniform line spacing plane gratings are introduced into a recording system to generate aspherical wavefronts for recording varied line spacing plane holographic gratings. Analytical expressions of groove parameters are derived to the fourth order. A ray-tracing validation algorithm is provided based on Fermat's principle and a local search method. The recording parameters are optimized to record a varied line spacing plane holographic grating with the aid of derived analytical expressions. A design example demonstrates the exactness of the analytical expressions and the superiority of recording optics with auxiliary gratings.     

Geometric theory of the ellipsoidal grating

A third-order geometric aberration theory of the ellipsoidal grating has been developed by analytically following an exact ray-tracing formalism with the aid of power series expansions. The theory takes into account all the possible aberrations up to third order and provides analytic formulas for the spot diagram of a spectral image formed by a modified or a nonmodified ellipsoidal grating with any of the groove patterns producible by means of mechanical ruling or conventional holographic recording. The present analytic formulas and other analytic ray-deviation formulas used in designing grating instruments have been evaluated in comparison with exact ray tracing. The results show the validity of the present theory and the limitation of the ray-deviation formulas based on the light path function and wave-frontaberration theory.     

Fabrication and evaluation of a wideband multilayer laminar-type holographic grating for use with a soft-x-ray flat-field spectrograph in the region of 1.7 keV

A multilayer laminar-type holographic grating having an average groove density of 2400 lines/mm is designed and fabricated for use with a soft-x-ray flat-field spectrograph covering the 0.70-0.75 nm region. A varied-line-spaced groove pattern is generated by the use of an aspheric wavefront recording system, and laminar-type grooves are formed by a reactive ion-etching method. Mo/SiO2 multilayers optimized for the emission lines of Hf-M, Si-K, and W-M are deposited on one of the three designated areas on the grating surface in tandem. The measured first-order diffraction efficiencies at the respective centers of the areas are 18%-20%. The flat-field spectrograph equipped with the grating indicates a spectral linewidth of 8-14 eV for the emission spectra generated from electron-impact x-ray sources.     

Third-generation holographic Rowland mounting: fourth-order theory

The third-generation holographic Rowland mount consists of a Rowland-mounted, optimally recorded holographic spherical grating, referred to as an optimized Rowland grating (ORG), whose recording sources are aberrated by two auxiliary ORG's. The main purpose of this mount is to avoid any aspherical surface while providing control over all the parameters needed to correct the aberrations up to and including the fourth order. Earlier [Appl. Opt. 30, 4019-4025 (1991)], we considered the case of a moderate coma c2. We now give the fourth-order theory, apply it to the high-dispersion (4600 grooves/mm) grating considered previously, and obtain for it diffraction-limited images.     

Holographic gratings for the Far Ultraviolet Spectroscopic Explorer: development, imaging, and efficiency tests of two prototypes

We report on a study and test of two 6000-groove/mm prototype holographic gratings for NASA's FarUltraviolet Spectroscopic Explorer (FUSE) mission. The first grating was designed and developed onthe basis of the FUSE requirements as specified at the end of the first study in 1992. This design relieson an ellipsoidal grating, recorded with aberrated wave fronts to correct sagittal coma. The secondgrating corresponds to the new design adopted after the complete mission was restructured in1993. With this solution a new family of spherical holographic gratings recorded with stigmaticsources was permitted to increase the aperture size while simplifying the figuring and recording of theblank. The design, fabrication, and testing of each prototype are described, and we show that thechallenging requirement of a 30,000 resolving power at 1000 ?, with a 25% groove efficiency, is reached.     

Wave-front recovery from two orthogonal sheared interferograms

We present a new technique for using the information of two orthogonal lateral-shear interferograms to estimate an aspheric wave front. The wave-front estimation from sheared inteferometric data may be considered an ill-posed problem in the sense of Hadamard. We apply Thikonov regularization theory to estimate the wave front that has produced the lateral sheared interferograms as the minimizer of a positive definite-quadratic cost functional. The introduction of the regularization term permits one to find a well-defined and stable solution to the inverse shearing problem over the wave-front aperture as well as to reduce wave-front noise as desired.     

Holographic imaging and interferometry with non-Bragg diffraction orders on volume and surface-relief gratings in lithium niobate and photo-thermoplastic materials

The recording of holographic volume and surface-relief gratings in a photorefractive crystal using a photo-thermoplastic (PTP) holographic camera with an image-bearing signal beam leads to the appearance of two Bragg and two or more non-Bragg diffracted beams that show the transformed images in each beam (rotation and angular amplification of images). Using this real-time mode of interferometry, the hologram is retrieved with a deformed object beam, resulting in the appearance of fringes with a proper phase shift in each of four diffracted beams. This one-shot (one-exposure) phase-shifting interferometry results in clarification of the object wave-front information (for example, from surface deformation) and solution of the sign ambiguity problem. This procedure demonstrates that high-resolution holographic imaging of the PTP holographic camera static deformations in the order of ～0.1?mm can be revealed on the diffusion reflection surface. In addition, it was demonstrated that using the PTP materials could achieve holographic recording and imaging through phase aberration, with the image appearing in the non-Bragg diffraction order.     

Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch-Zernike polynomials

Recording methods for making aberration-corrected holographic gratings are greatly simplified by use of a plane multimode deformable mirror (MDM) upon one of the two recording beams. It is shown that MDM compensators easily provide the superposition of many interesting active optics modes, which we have named Clebsch-Zernike modes. When we apply only a uniform loading or no loading at all onto the rear side of the MDM clear aperture, the available Clebsch-Zernike modes are made to belong to a subclass of the Zernike modes that includes the three modes of the third-order aberration theory as well as a well-defined part of the Zernike higher-order modes. Such a recording method is considered to be universal, since it does not require the use of a sophisticated optical system such as a compensator. Active optics 12-arm MDM's in the vase form have been designed from the elasticity theory. The design of six-arm MDM's is currently carried out with theoretical results. As an example of the method, the recording of three holographic gratings of the Hubble Space Telescope Cosmic Origins Spectrograph has been investigated. Substantial improvements in image quality have been found by use of a six-arm MDM as recording compensator. The result is that aberrations of much higher order can simultaneously be corrected so that the residual blur images of the spectra occupy areas approximately 10 (direction of dispersion) x 3 (cross dispersion) = 30 times smaller-also in terms of pixel number-than those obtained by our American colleagues. Therefore the active optics recording method appears to provide substantial gains in resolving power and in sensitivity: (i) For all three gratings the spectral resolution would be increased by a factor of 10, and (ii), in addition, for the two higher dispersion gratings, the limiting magnitude on the sky appears to be increased by a magnitude of approximately 1-1.2.     

Optical fringe multiplication in moiré interferometry

An optical method for multiplication of moiré fringes is proposed to increase the sensitivity of moireé interferometry. The process involves two recording steps. In the first step, a traditional moiré interferometry setup is used. The moiré pattern containing carrier fringes and load fringes is recorded onto a glass-based holographic plate. The carrier frequency is much lower than that of the original specimen grating. The plate is then developed. In the second step, the holographic plate, regarded as a distorted specimen grating, is further examined by a similar moiré interferometry system. The frequency of the second virtual grating is arranged to be 2n times that of the carrier fringes contained in the recorded plate. As a result, the load fringes are revealed with a multiplication factor of 2n. The interpretation of the optical multiplication method from wave-front interference theory is given and an experiment is conducted.     

High-dispersion spherical holographic gratings in a modified rowland mounting

For holographic gratings requiring an extreme dispersion, I consider a modified Rowland mounting, in which the recording laser sources are moved away from the grating, to reduce the uncorrected higher-order aberrations. In addition, I choose the geometric parameters such that first-type coma is corrected. Then a plane multimode deformable mirror (MDM) or two auxiliary spherical holographic gratings (R3 device) are used to aberrate the grating's recording sources; correction up to the fourth order is sufficient to obtain high image quality. Applied to the FUSE-Lyman (FUSE is Far Ultraviolet Spectroscopic Explorer) grating, with a groove density as high as 5767 grooves/mm, these recording devices produce a resolution (chromatic resolving power) as great as 611,000 with the MDM and 3,030,000 with the R3 device. These results far exceed the specified performance of 30,000. Since diffraction limits the resolution to 482,000, the images are diffraction limited with both devices.     

Filtering theory and application of wavelet optics at the spatial-frequency domain

We propose a wave-front filtering concept of wavelet optics and present its associated theory of wavelet optics. We analyze the filtering phenomenon of wavelet optics at the spatial-frequency domain-multiscale edge detection and multiscale feature recognition-using the theory, and we also perform the analysis with the Mexican-hat wavelet and the Haar wavelet. By use of our theory, information is obtained from an optical image that is processed multiscalely and delicately by stretching and translation of the factors. With this technique it is possible to perform real-time programming in information processing in a mixed optical system.     

Phase-locked-loop interferometry applied to aspheric testing with a computer-stored compensator

A recently developed technique for continuous-phase determination of interferograms with a digital phase-locked loop (PLL) is applied to the null testing of aspheres. Although this PLL demodulating scheme is also a synchronous or direct interferometric technique, the separate unwrapping process is not explicitly required. The unwrapping and the phase-detection processes are achieved simultaneously within the PLL. The proposed method uses a computer-generated holographic compensator. The holographic compensator does not need to be printed out by any means; it is calculated and used from the computer. This computer-stored compensator is used as the reference signal to phase demodulate a sample interferogram obtained from the asphere being tested. Consequently the demodulated phase contains information about the wave-front departures from the ideal computer-stored aspheric interferogram. Wave-front differences of ~ 1 λ are handled easily by the proposed PLL scheme. The maximum recorded frequency in the template's interferogram as well as in the sampled interferogram are assumed to be below the Nyquist frequency.     

Visor-display design based on planar holographic optics

A method for designing and recording visor displays based on planar holographic optics is presented. This method can deal with the problem of recording-readout wavelength shift. The display system is composed of two holographic optical elements that are recorded on the same substrate. One element collimates the waves from each data point in the display into a plane wave that is trapped inside the substrate by total internal reflection. The other diffracts the plane waves into the eye of an observer. Because the chromatic dispersion of the first element can be corrected by the dispersion of the second, this configuration is relatively insensitive to source wavelength shifts. The method is illustrated by the design, recording, and testing of a compact holographic doublet visor display. The recording was at a wavelength of 458 nm, and readout was at 633 nm. The results indicate that diffraction-limited performance and relatively low chromatic dispersion over a wide field of view can be obtained.     

Geometric view of adaptive optics control

The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A 73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures.     

Hierarchical wave-front sensing

We present a new wave-front sensing technique for adaptive optics based on use of several wave-front sensors dedicated to the sensing of a different range of spatial frequencies. We call it a hierarchical wave-front sensor. We present the concept of a hierarchical wave-front sensor and apply it to the Shack-Hartmann sensor. We show the gain that is expected with two Shack-Hartmann sensors. We obtain a gain that increases with the size of the largest sensor, and we detail the application of hierarchical wave-front sensing to extreme adaptive optics and extremely large telescopes.     

Design of a nonnull interferometer for aspheric wave fronts

The presence of highly aspheric wave fronts in an interferometer leads to a need for system calibration, and this calibration requirement affects the design of the interferometer. Dynamic range, vignetting, and the ability to characterize components all must be considered during the design stages. The interferometer must be designed with respect to wave-front propagation as opposed to reference sphere aberrations. A nonnull interferometer for measurement of aspheric transmitted wave fronts has been developed, and the design process is described. Transmitted wave fronts for a conformal window and a progressive-addition bifocal lens have been measured to demonstrate the applicability of the system to aspheric testing.     

Potential and limits of holographic reconstruction algorithms

For the purpose of ultrasonic nondestructive testing of materials, holography in connection with digital reconstruction algorithms has been proposed as a modern tool to extract crack sizes from ultrasonic scattering data. Defining the typical holographic reconstruction algorithm as the application of the scalar Kirchhoff diffraction theory to backward wave propagation, we demonstrate its general incapability of reconstructing equivalent sources, and hence, geometries of scattering bodies. Only the special case of a planar measurement recording surface, that is to say, a hologram plane, and a planar crack with perfectly rigid boundary conditions parallel to the hologram plane and perpendicular to the incident field yields a nearly perfect correlation between crack size and reconstructed image; the reconstruction algorithm is then referred to as the Rayleigh-Sommerfeld formula; it therefore represents the optimal case matched to that special geometrical situation and, hence, may be interpreted as a quasi-matched spatial filter. Using integral equation theory and physical optics, we compute synthetic holographic data for a linear cracklike scatterer for both plane and spherical wave incidence, the latter case simulating a synthetic aperture impulse echo situation, thus illustrating how the Rayleigh-Sommerfeld algorithm or its Fresnel approximation increasingly fail for cracks inclined to the hologram plane and excited nonperpendicularly. Furthermore, we point out how the physical data recording process may additionally influence the reconstruction accuracy, and, finally, guidelines for a careful and serious application of these holographic reconstruction algorithms are given. The theoretical results are supported by measurements.     

High-speed, acousto-optically addressed optical memory

A page-oriented, angle-multiplexed volume holographic optical-memory recording system has been constructed. This memory is addressed by the use of an acousto-optic deflector with a random-access time of 16 μs per page. This enables data transfer rates of 5.28 Gbits/s when pages of binary data are being stored. The reconstruction quality of images stored as memory pages is assessed with the quality achieved with the acousto-optic device compared with that achieved with the original recording optics.     

Design of a holographic optical element for a pulse compressor

Nonlinear chirped pulse compression can be theoretically achieved to any order by using a nonplane grating with adequate groove spacing. We evaluate the holographic recording of a grating that compensates to the quadratic chirp. A suitable design is found, and the building tolerances are analyzed.