Modulation depth of Michelson interferometer with Gaussian beam

Mirror misalignment or the tilt angle of the Michelson interferometer can be estimated from the modulation depth measured with collimated monochromatic light. The intensity of the light beam is usually assumed to be uniform, but, for example, with gas lasers it generally has a Gaussian distribution, which makes the modulation depth less sensitive to the tilt angle. With this assumption, the tilt angle may be underestimated by about 50%. We have derived a mathematical model for modulation depth with a circular aperture and Gaussian beam. The model reduces the error of the tilt angle estimate to below 1%. The results of the model have been verified experimentally.     

Wave-front tilt sensor with two quadrant detectors and its application to a laser beam pointing system

A method that uses two quadrant detectors (QDs) for sensing wave-front tilt is described. The detectors are set at the front and back of the focal plane of the focusing optics. When the intensity distribution at the aperture of a telescope is not uniform because of atmospheric turbulence, the wave-front tilt can be measured more accurately with our two-QD method than with a conventional single-focal-plane QD. We proved this method to be effective by using it for fixed-star observation. Application of the method to a ground-to-satellite laser beam pointing system showed that it increases the intensity of the laser beam that is transmitted to a satellite.     

Serrated-aperture apodizers for high-energy laser systems

Spatial beam apodization is a critical part of the design of high-energy solid-state laser systems. Standard methods of making apodizers include photographic and metal-vapor-deposition techniques. Apodizers fabricated with these methods are subject to damage and deterioration from high-intensity laser pulses. An alternative approach is to use a serrated-edge aperture in conjunction with the spatial filter. This system can produce beams with smooth edge profiles. We present the theory of operation of the serrated aperture along with some useful design rules and describe the successful application of a serrated-aperture apodizer in the Beamlet laser system.     

Experimental study of the effect of surface defects on the finesse and contrast of a Fabry-Perot interferometer

While investigating the instrumental function of a Fabry-Perot interferometer [Appl. Opt. 34, 58 (1995), we noticed some variation in finesse and contrast in the measured spectra when a 1.5-mm-diameter aperture was used at various spots within the standard 8-mm aperture. By comparing experimentally determined finesse versus contrast plots for many such spectra with calculated plots, we found spots on the plates that gave non-Airy-function line shapes over the entire order of interference, unlike the Airy line shape we determined previously by using the entire 8-mm aperture. We have reviewed several models that describe the effects of various types of surface defects, such as Gaussian-height distribution of roughness, curvature and tilt of plates, sinusoidal roughness, and asymmetrical roughness on the finesse and contrast. Our experimental results can be accounted for if we assume that the reflectivity is nonuniform over the Fabry-Perot plates and that there is some reasonable contribution that is due to Gaussian roughness, curvature, or tilt.     

Incorporating higher-order modal measurements in tilt estimation: natural and laser guide star applications

Tilt compensation performance is generally suboptimal when phase measurements from natural or laser guide stars are used as the conjugate phase in an adaptive optics system. Optimal compensation is obtained when the conjugate-phase coefficients are estimated from beacon measurements, given knowledge of the correlation between the on-axis object phase and the beacon measurements. We apply optimal compensation theory to tilt correction for the case of an off-axis beacon. Because off-axis higher-order modes are correlated with the on-axis tilt components, a performance gain can be realized when the tilt estimator includes higher-order modal measurements. For natural guide star compensation, it is shown that equivalent tilt compensation can be achieved at beacon offsets that are three times larger when higher-order modes through Zernike 15 are used in the tilt estimator. For a laser guide star, although tilt information cannot be measured directly because of beam reciprocity, off-axis higher-order modal measurements can be used to estimate tilt components, leading to a maximum Strehl ratio of approximately 0.3 for the relative aperture diameter D/r(0) = 4 and the relative turbulence outer scale L(0)/D = 10.     

Problem of track offset in optical disk systems

In an optical disk drive, it is well known that a tilt of the disk causes an offset in the tracking-error signal (TES). One effect of disk tilt is the introduction of a dc component to the TES, which can be largely corrected by operation of the tracking system at the midpoint between the maximum and the minimum values of the open-loop TES. However, this method of correcting for the dc shift in the TES does not correct for the effect of coma in the focused spot, which leads to track offset. The track offset of a system is defined as the distance between the peak irradiance in the focused spot and the center of the groove when the tracking system is operating at the midpoint between the maximum and the minimum values of the open-loop TES in the presence of disk tilt. Calculations are performed that show the dependence of track offset on various system parameters, including track pitch, wavelength, and numerical aperture and rim intensity of the objective lens, and on the regions of the beam used to generate the TES. The track offsets for several beam-segmentation schemes are calculated for a digital versatile disk that uses push-pull and differential phase tracking. It is shown that for differential phase tracking the value of track offset depends on the mark length.     

Approximate phase conjugation with a retroreflecting array in microscopy

Some experiments on image recovery in microscopy are described. The aperture stop of a microscope objective is partially obscured, and a retroreflecting array is used as an approximate phase conjugator to return the beam through the unobstructed part of the aperture. An application is made to the measurement of the absolute reflectance of small samples by use of a variant of Strong's method.     

Dove prism with increased throughput for implementation in a rotational-shearing interferometer

An analytical expression is derived for the tilt introduced into a wave front by a Dove prism with manufacturing errors in the prism's base angles and pyramidal angle. We found that the tilt decreases when the base angles are increased above the values of traditional design. The increase in the length-aperture ratio of a prism is detrimental to the prism's performance. However, a Dove prism with a widened aperture increases throughput and maintains a manageable prism weight for implementation in a rotational shearing interferometer. Thus we propose a Dove prism designed with a widened aperture to increase throughput in a rotational shearing interferometer and with larger base angles to minimize the wave-front tilt introduced by manufacturing errors. Experimental results implemented in a rotational shearing interferometer demonstrate the feasibility of this design.     

Beam steering experiment with two cascaded ferroelectric liquid-crystal spatial light modulators

The design, construction, and evaluation of a laser beam steerer that uses two binary ferroelectric liquid-crystal (FLC) spatial light modulators (SLMs) operated in conjunction are presented. The system is characterized by having few components and is in principle lossless. Experimentally, a throughput of approximately 20% was achieved. The simple system design was achieved because of the high tilt angle FLC material used in the SLMs, which were specifically designed and manufactured for this study. By coherently imaging the first SLM onto the second SLM, pixel by pixel, we obtained an effective four-level phase structure with a phase step of 90 degrees. An appropriate alignment procedure is presented. The beam steering performance of the system is reported and analyzed.     

Tilt angular anisoplanatism and a full-aperture tilt-measurement technique with a laser guide star

A method is presented for sensing atmospheric wave-front tilt from a laser guide star (LGS) by observing a laser beacon with auxiliary telescopes. The analysis is performed with a LGS scatter model and Zernike polynomial expansion of wave-front distortions. It is shown that integration of the LGS image over its angular extent and the position of the auxiliary telescope in an array reduce the tilt sensing error associated with the contribution from the downward path. This allows us to single out only the wave-front tilt of the transmitted beam on the uplink path that corresponds to the tilt for the scientific object. The tilt angular correlation is analyzed in the atmosphere with a finite turbulence outer scale. The tilt correlation angle depends on the angular size of the telescope and the outer scale of turbulence. The tilt sensing error increases with the auxiliary telescope diameter, suggesting that an auxiliary telescope must be small. The Strehl ratio associated with the contribution from the downward path is in the range from 0.1 to 0.9 when the relative telescope diameter D/r(0) varies from 4 to 93 and the turbulence outer scale is in the 10-150-m range. Tilt correction increases the Strehl ratio compared with the uncorrected image for all the system parameters and seeing conditions considered. The method discussed gives a higher performance than the conventional technique, which uses an off-axis natural guide star. A scheme for measuring tilt with a beam projected from a small aperture is described. This scheme allows us to avoid phosphorescence of the main optical train for a sodium LGS.     

Tracking in a ground-to-satellite optical link: effects due to lead-ahead and aperture mismatch, including temporal tracking response

Establishing a link between a ground station and a geosynchronous orbiting satellite can be aided greatly with the use of a beacon on the satellite. A tracker, or even an adaptive optics system, can use the beacon during communication or tracking activities to correct beam pointing for atmospheric turbulence and mount jitter effects. However, the pointing lead-ahead required to illuminate the moving object and an aperture mismatch between the tracking and the pointing apertures can limit the effectiveness of the correction, as the sensed tilt will not be the same as the tilt required for optimal transmission to the satellite. We have developed an analytical model that addresses the combined impact of these tracking issues in a ground-to-satellite optical link. We present these results for different tracker/pointer configurations. By setting the low-pass cutoff frequency of the tracking servo properly, the tracking errors can be minimized. The analysis considers geosynchronous Earth orbit satellites as well as low Earth orbit satellites.     

Calculation and correction of subaperture tilt aberration modes in synthesis imaging

We extend the redundant spacings calibration method for finding piston coefficients affecting the elements of a dilute aperture array so that tilt phase coefficients can also be calculated and corrected without the need for assumptions about the object. The tilt coefficient retrieval method is successfully demonstrated in simulation, and the specifics of correction by image sharpness are discussed, showing that in dilute aperture systems this method does not necessarily produce a unique image.     

Power collection of a laser diode elliptical beam by a decentered circular aperture

The elliptical beam of a laser diode is collected by a circular aperture decentered with respect to the beam. The fractional optical power collected is calculated and measured as a function of the decentered distance, beam size, and aperture size. The calculation results agree well with the measurement results. An application example of the results is described.     

计量型紫外显微镜实时焦点及倾角测量算法的研究

计量型紫外光学显微镜采用248 nm深紫外光源和高数值孔径物镜系统,工作距离和景深均很小,为实现清晰的成像,需要进行自动聚焦。因此研究了一种焦点及倾角测量算法,采用基于图像处理的自动聚焦方法,选择Tenengrad函数作为图像清晰度判据,进行清晰度评价。针对在扫描测量时标准样板倾斜与镜片可能会出现相撞的问题,提出了样板倾角测量方法来判断样板的倾斜方向和角度,从而确定物镜执行器的移动方向,实现物镜扫描成像过程中的动态对焦。     

Propagation of decentered elliptical Gaussian beams in apertured and nonsymmetrical optical systems

A hard-edged elliptical aperture is described approximately by a tensor form, which can be expanded as a finite sum of complex Gaussian functions. An analytical propagation expression for a decentered elliptical Gaussian beam (DEGB) through an axially nonsymmetrical optical system with an elliptical aperture is derived by using vector integration. The approximate analytical results are compared with numerically integral ones, and it is shown that this method can significantly improve the efficiency of numerical calculation. Some numerical simulations are illustrated for the propagation properties of DEGBs through apertured and nonsymmetrical optical transforming systems.     

Interferometric phase reconstruction by nonuniform shifting of the reference beam

A method for phase measurement in common-path interferometers, believed to be novel, is presented. We use the property of phase reconstruction algorithms, such as the Carré and Hariharan algorithms, that do not require uniform phase across the reference beam. Only the ratio of the phase steps must be the same at each pixel. We show phase measurement and reconstruction in a common-path interferometer by shifting either the tilt or the focus of the reference wave front. We present a theoretical explanation of phase measurement using this property. We also present results from a proof-of-principle experiment using a scatterplate interferometer, in conjunction with the tilt phase-shifting technique, to measure the reflected phase of a test optical element. Furthermore, we present a computer simulation to demonstrate the mathematical validity of this measurement technique using defocus shifting, rather than tilt shifting, in the reference wave front.     

Formation of speckle images formed for diffusers illuminated by modulated apertures (circular obstruction)

An amplitude modulation of circular aperture is used for the illumination of a numerical object having a randomly distributed function. In this study, a central obstruction for the aperture is assumed. The modulated speckle image is obtained using the MATLAB program and compared with that obtained in the case of an uniform circular aperture for the illumination. We have considered coherent illumination obtained from a laser beam in order to facilitate the computation of the Fourier transform of the defined computed speckle intensity corresponding to this novel aperture. Finally, the autocorrelation function of the randomly distributed object is calculated in all cases.     

Generation of a flat-top laser beam for gravitational wave detectors by means of a nonspherical Fabry-Perot resonator

We have tested a new kind of Fabry-Perot long-baseline optical resonator proposed to reduce the thermal noise sensitivity of gravitational wave interferometric detectors--the "mesa beam" cavity--whose flat top beam shape is achieved by means of an aspherical end mirror. We present the fundamental mode intensity pattern for this cavity and its distortion due to surface imperfections and tilt misalignments, and contrast the higher order mode patterns to the Gauss-Laguerre modes of a spherical mirror cavity. We discuss the effects of mirror tilts on cavity alignment and locking and present measurements of the mesa beam tilt sensitivity.     

Elevation performance of 1.25D and 1.5D transducer arrays

Present 1D phased array probes have outstanding lateral and axial resolution, but their elevation performance is determined by a fixed aperture focused at a fixed range. Multi-row array transducers can provide significantly improved elevation performance in return for “modest” increases in probe and system complexity. Time domain simulations of elevation beam profiles are used to compare several types of multi-row probes. The elevation aperture of a 1.25D probe increases with range, but the elevation focusing of that aperture is static and determined principally by a mechanical lens with a fixed focus (or foci). 1.25D probes can provide substantially better near- and far-field slice thickness performance than 1D probes and require no additional system beamformer channels. 1.5D, probes use additional beamformer channels to provide dynamic focusing and apodization in elevation. 1.5D probes can provide detail resolution comparable to, and contrast resolution substantially better than, 1.25D probes, particularly in the mid- and far-field. Further increases in system channel count allow the use of 1.75D and 2D arrays for adaptive acoustics and two-dimensional beam steering. Significant improvements in clinical image quality can be expected as multi-row probes become increasingly available in the marketplace     

Dark field imaging of semicrystalline polymers by scanning transmission electron microscopy

Scanning transmission electron microscopy (STEM) has been suggested to have advantages over conventional transmission electron microscopy (CTEM) for the observation of diffraction contrast features and diffraction patterns from radiation sensitive crystalline polymers. Because of image intensification, control of illumination location and magnification independent focus, STEM operation for focusing, area selection and set up of optics permits a high yield of systematic data. Dark field (DF) imaging is most useful when employed in conjunction with scanning microarea diffraction. For convergent beam microdiffraction and efficient DF imaging of thin crystals the beam divergence should be less than 5×10^–3 radians. For single beam DF, the reflection of interest is selected by the intermediate lens aperture. Use of a STEM annular detector to collect more than one reflection results in increased DF image intensity and resolution. Use of the entire azimuthal range of a single powder pattern reflection permits examination of crystal texture — in particular, images produced by chain axis reflections show the detailed arrangements of lamellae.