Possibilities for correcting aberrations of imaging laser systems by phase conjugation

The reported method of using phase conjugation to correct distortions induced by projection optics was realized experimentally. In particular, the method was used on a low-quality 50-cm-diameter objective mirror to form laser radiation with a near diffraction-limited beam divergence of 2.4 × 10(-6) rad. The method could be applied to high-resolution imaging of objects in coherent light.     

Parabolic mirror optics for collimation of a crescent blue laser beam radiated from channel waveguide Čerenkov second-harmonic generation

Parabolic mirror optics to collimate the crescent-shaped blue laser beam that radiates from ?erenkov second-harmonic generation (SHG) in a channel waveguide configuration is proposed. Mirror collimation optics has a large tolerance to the variations of SHG element parameters, such as the laser source wavelength, as well as to mirror displacement. The anisotropy of a nonlinear crystal in which the waveguide is fabricated has been taken into account. The optimum mirror alignment to obtain a collimated blue laser beam is evaluated in terms of Marechal's criterion. The minimum wave-front aberration with beam intensity weighted is 0.054 λSH. The convergence of the collimated beam is less than 1.6 mrad, and, by using an objective lens, the collimated beam can be focused to a diameter of less than 1 μm, which is 1.27 times the diffraction-limited focusing point.     

Camera for coherent diffractive imaging and holography with a soft-x-ray free-electron laser

We describe a camera to record coherent scattering patterns with a soft-x-ray free-electron laser (FEL). The camera consists of a laterally graded multilayer mirror, which reflects the diffraction pattern onto a CCD detector. The mirror acts as a bandpass filter for both the wavelength and the angle, which isolates the desired scattering pattern from nonsample scattering or incoherent emission from the sample. The mirror also solves the particular problem of the extreme intensity of the FEL pulses, which are focused to greater than 10(14) W/cm2. The strong undiffracted pulse passes through a hole in the mirror and propagates onto a beam dump at a distance behind the instrument rather than interacting with a beam stop placed near the CCD. The camera concept is extendable for the full range of the fundamental wavelength of the free electron laser in Hamburg (FLASH) FEL (i.e., between 6 and 60 nm) and into the water window. We have fabricated and tested various multilayer mirrors for wavelengths of 32, 16, 13.5, and 4.5 nm. At the shorter wavelengths mirror roughness must be minimized to reduce scattering from the mirror. We have recorded over 30,000 diffraction patterns at the FLASH FEL with no observable mirror damage or degradation of performance.     

Wave-front design algorithm for shaping a quasi-far-field pattern

To design a fully continuous wave-front distribution suitable for focused beam shaping by a deformable mirror, we modify the phase-retrieval algorithm by employing a uniformly distributed phase as a starting phase screen and spatial filtering for the near-field phase retrieved during the iteration process. A special phase unwrapping algorithm is not required to obtain a continuous phase distribution from the retrieved phase since the boundary of the 2pi-phase-jumped region in the designed phase distribution is perfectly closed. From the computational result producing a uniform square beam transformation from a circular defocused beam, this algorithm has provided a fully continuous wave-front distribution with a lower spatial frequency for a deformable mirror. The transformed square beam has a normalized intensity nonuniformity of varsigma(rms) = 0.14 with respect to a desired flat-topped square beam pattern. This beam-shaping method also provides a high energy-concentration rate of more than 98%.     

Designing reflectors to generate a line-shaped directivity diagram

A novel method of designing a mirror surface to generate a directivity diagram represented as a vector function of one argument is presented. A general relationship for the mirror surface for an arbitrary illuminating beam wavefront is derived as an envelope of a parametric family of surfaces. Each surface in the family transforms the input beam into a beam with plane wavefront of desired direction. For the spherical illuminating beam the mirror surface is given as the envelope of the family of rotational paraboloids. The envelope is represented as a family of curves given by the intersections of paraboloids with circular cones of rays from the point source.     

Single-mirror beam steering system: analysis and synthesis of high-order conic-section scan patterns

The vector approach introduced in an early paper for modeling mirror-scanning devices [Y. Li, Appl. Opt. 34, 6417 (1995)] provides the basis of a rigorous study of the scan field generated by a single-mirror beam steering system, in which a hinged movable mirror is able to turn about a fixed pivot point to steering a single laser beam. Because of fewer constraints on mirror angular motion, the system may behave like a true point source for both vector and raster scanning applications. After a summary of the expressions for scan fields generated under different conditions, some fundamental and advanced topics of the single-mirror system are addressed: (1) basic parameters of high-order conic-section scan patterns, (2) scanning spot kinematics, (3) effect of input offset and pixels distortions on two-dimensional images displayed on screens of different formats, (4) mapping and its inverse between the mirror vector space and the scan vector space, and (5) single-mirror beam steering system as a one-element reflective and continuous image zooming device.     

Folding mirror schlieren diffraction interferometer

We demonstrate the use of a mirror as a viewing diaphragm to generate a built-in diffracted reference beam in schlieren diffraction interferometry (SDI). The use of a mirror edge as a diffracting element instead of a conventional knife edge considerably enhances the contrast of the schlieren pattern, and it is shown to be equal to that of a phase knife edge. This increase in contrast is due to the fact that the otherwise unutilized diffracted beam in SDI is recombined in the described folding mirror geometry.     

Dynamic Correction of Thermal Focusing in Nd:YAG Confocal Unstable Resonators by Use of a Variable Radius Mirror

Excellent beam quality and divergence stability over a wide pump power range was demonstrated in a Q-switched, Nd:YAG, positive branch confocal unstable resonator by using a one degree-of-freedom, adaptive optic. Unlike single-element flexible-membrane mirrors, the variable radius mirror (VRM) consisted of a lens and mirror, whose separation determined the VRM's effective radius of curvature. This simple method enabled low cost and efficient thermal focusing compensation. The VRM was demonstrated by producing a 300-mJ Q-switch or 1-J free-running at a beam quality factor M(2) that varied between 1.2 and 1.8 as the average output power varied between 0 and 33 W.     

Optimum control of the laser beam intensity profile with a deformable mirror

A new deformable mirror control system is developed. This system consists of a deformable mirror, a CCD camera, an image processor, a computer, and actuator drive power supplies. A genetic algorithm is adopted as a control algorithm to obtain an optimum surface profile of the deformable mirror. A circular cross-sectional Gaussian beam was transformed into a beam with a rectangular contour using this system. Although the transfer function of this system is complicated and unknown, this system can be used to obtain the optimum beam profile within the achievable limits of a deformable mirror.     

Polarimetric calibration of large-aperture telescopes. I. Beam-expansion method

A concept is described for the high-accuracy absolute calibration of the instrumental polarization introduced by the primary mirror of a large-aperture telescope. This procedure requires a small aperture with polarization-calibration optics (e.g., mounted on the dome) followed by a lens that opens the beam to illuminate the entire surface of the mirror. The Jones matrix corresponding to this calibration setup (with a diverging incident beam) is related to that of the normal observing setup (with a collimated incident beam) by an approximate correction term. Numerical models of parabolic on-axis and off-axis mirrors with surface imperfections are used to explore the accuracy of the procedure.     

Use of null optics for monitoring the optical alignment of a beam director

The use of null optics is proposed as a new concept for monitoring the optical alignment of a beam director. Null optics consist of a primary mirror and an annular mirror just outside the aperture of the secondary mirror. The characteristics of the proposed null optics are investigated with the designed sample of a two-mirror system with an effective aperture of 275 mm. The results show that null optics yield four times the amplification with respect to the alignment errors of the secondary mirror; however, they have low residual aberration sensitivity to misalignment. Therefore null optics can be used successfully as the alignment monitoring apparatus of a beam director.     

Multipass open-path Fourier-transform infrared measurements for nonintrusive monitoring of gas turbine exhaust composition

The detection limits for NO and NO2 in turbine exhausts by nonintrusive monitoring have to be improved. Multipass mode Fourier-transform infrared (FTIR) absorption spectrometry and use of a White mirror system were found from a sensitivity study with spectra simulations in the mid-infrared to be essential for the retrieval of NO2 abundances. A new White mirror system with a parallel infrared beam was developed and tested successfully with a commercial FTIR spectrometer in different turbine test beds. The minimum detection limits for a typical turbine plume of 50 cm in diameter are approximately 6 parts per million (ppm) for NO and 9 ppm for NO2 (as well 100 ppm for CO2 and 4 ppm for CO).     

Intracavity generation of radially polarized CO2 laser beams based on a simple binary dielectric diffraction grating

We present experimental results on the intracavity generation of radially polarized light by incorporation of a polarization-selective mirror in a CO(2)-laser resonator. The selectivity is achieved with a simple binary dielectric diffraction grating etched in the backsurface of the mirror substrate. Very high polarization selectivity was achieved, and good agreement of simulation and experimental results is shown. The overall radial polarization purity of the generated laser beam was found to be higher than 90%.     

Laser beam intensity profile transformation with a fabricated mirror

A nonaxisymmetric mirror is designed by the same method as a computer-generated hologram for laser beam intensity profile transformation and is fabricated by plasma chemical vaporization machining. We successfully transformed a circular Gaussian beam of a He-Ne laser into a rectangular uniform beam maintaining spatial coherence and using a nonaxisymmetric surface profile mirror. There are ripples in the intensity profile of the transformed rectangular beam. These ripples in the intensity profile result from small ripples on the mirror surface. These results show that we can perform coordinate transformation using these fabricated mirrors, which has so far been possible only by using computer-generated holograms.     

Imaging a point to a line with a single spherical mirror

Methods for imaging a single point source to a line image are discussed, and a design study of single spherical mirror systems that form aberration-free line images is presented. An expression forthe ray density along the line image is derived for such systems in the cases of (i) uniform beam profiles and (ii) Gaussian beam profiles. The resulting ray density profiles are illustrated for single spherical mirror systems over a wide range of design parameters.     

A phase-conjugate Twyman-Green interferometer with increased sensitivity for laser beam collimation

Abstract

A Twyman-Green interferometer having a phase-conjugate mirror in one arm and double mirror in another arm is described to measure divergence and to check the collimation of a laser beam. It uses an internally self-pumped phase conjugation in BaTiO₃ crystal as phase-conjugate mirror. The use of double mirror gives a dual interference field which results in improved sensitivity in collimation testing. The dual-field interferogram is also useful in easily distinguishing between the divergent and convergent nature of the test beam. Measurement results are presented.     

Two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere

A two-deformable-mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier-transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained with a technique based on the Fienup phase-retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable-mirror system, this field-conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared with a conventional phase-only correction system.     

Observation of enhanced backscattering from a plane mirror viewed through polymer-film-dispersed liquid crystals

We report experimental results on enhanced backscattering from a plane mirror that is viewed through polymer-film-dispersed nematic liquid crystals. The distribution of the averaged intensity of the light reflected from the mirror placed behind the polymer film is investigated with an image-processing system when a Gaussian beam wave is incident. The enhanced light peak is observed in an incident beam direction, the result of which is predicted by a theory based on the circular Gaussian statistic random-phase-screen model. We pay attention to the enhancement dependence on parameters such as the distance between the polymer film and the flat mirror. The observed result is similar to a previous study by Jakeman et al. in which a random diffusive glass plate was used as a random-phase screen [J. Phys. D 21, 32 (1988)].     

Measurement of glitter-point velocities on the sea surface using circular scanning with a collimated narrow laser beam

Alaser device (lidar) for remotely measuring the parameters of the glitter-point motion on the sea surface has been developed. The system employs a He-Ne laser to provide the probe beam. Circular scanning was performed by means of a piezoelectrically controlled mirror that had a frequency of rotation of 2 kHz. The positions of glitter-point echo pulses were compared with the reference signal of the mirror controller to trace the time evolution of the glitter-point coordinates on the circumference of the circular laser beam track. The measurements yielded the velocity distribution of the glitter points. The results were obtained under natural conditions and indicate an anisotropy of the glitter-point motion that is related to the sea conditions and the wind direction.     

Off-axis mirror based optical system design for circularization, collimation, and expansion of elliptical laser beams

In this paper, we present two optical system design methods for beam circularization, collimation, and expansion of semiconductor laser output beam for possible application in LIDAR systems. Two different optical mirror systems are investigated: an off-axis hyperbolic/parabolic mirror system and an off-axis parabolic mirror system. Equations specific to these mirror systems are derived and computer package programs such as ZEMAX and MATLAB are used to simulate the optical designs. The beam reshaping results are presented.