Wavefront Detection Research Articles

Automatic centroid detection and surface measurement with a digital Shack–Hartmann wavefront sensor

With the breakthrough of manufacturing technologies, the measurement of surface profiles is becoming a big issue. A Shack–Hartmann wavefront sensor (SHWS) provides a promising technology for non-contact surface measurement with a number of advantages over interferometry. The SHWS splits the incident wavefront into many subsections and transfers the distorted wavefront detection into the centroid measurement. So the accuracy of the centroid measurement determines the accuracy of the SHWS. In this paper, we have presented a new centroid measurement algorithm based on an adaptive thresholding and dynamic windowing method by utilizing image-processing techniques. Based on this centroid detection method, we have developed a digital SHWS system which can automatically detect centroids of focal spots, reconstruct the wavefront and measure the 3D profile of the surface. The system has been tested with various simulated and real surfaces such as flat surfaces, spherical and aspherical surfaces as well as deformable surfaces. The experimental results demonstrate that the system has good accuracy, repeatability and immunity to optical misalignment. The system is also suitable for on-line applications of surface measurement.

Differential modal Zernike wavefront sensor employing a computer-generated hologram: a proposal

The process of Zernike mode detection with a Shack-Hartmann wavefront sensor is computationally extensive. A holographic modal wavefront sensor has therefore evolved to process the data optically by use of the concept of equal and opposite phase bias. Recently, a multiplexed computer-generated hologram (CGH) technique was developed in which the output is in the form of bright dots that specify the presence and strength of a specific Zernike mode. We propose a wavefront sensor using the concept of phase biasing in the latter technique such that the output is a pair of bright dots for each mode to be sensed. A normalized difference signal between the intensities of the two dots is proportional to the amplitude of the sensed Zernike mode. In our method the number of holograms to be multiplexed is decreased, thereby reducing the modal cross talk significantly. We validated the proposed method through simulation studies for several cases. The simulation results demonstrate simultaneous wavefront detection of lower-order Zernike modes with a resolution better than lambda/50 for the wide measurement range of +/-3.5lambda with much reduced cross talk at high speed.

Adaptive thresholding and dynamic windowing method for automatic centroid detection of digital Shack-Hartmann wavefront sensor

A Shack-Hartmann wavefront sensor (SWHS) splits the incident wavefront into many subsections and transfers the distorted wavefront detection into the centroid measurement. The accuracy of the centroid measurement determines the accuracy of the SWHS. Many methods have been presented to improve the accuracy of the wavefront centroid measurement. However, most of these methods are discussed from the point of view of optics, based on the assumption that the spot intensity of the SHWS has a Gaussian distribution, which is not applicable to the digital SHWS. In this paper, we present a centroid measurement algorithm based on the adaptive thresholding and dynamic windowing method by utilizing image processing techniques for practical application of the digital SHWS in surface profile measurement. The method can detect the centroid of each focal spot precisely and robustly by eliminating the influence of various noises, such as diffraction of the digital SHWS, unevenness and instability of the light source, as well as deviation between the centroid of the focal spot and the center of the detection area. The experimental results demonstrate that the algorithm has better precision, repeatability, and stability compared with other commonly used centroid methods, such as the statistical averaging, thresholding, and windowing algorithms.

Beam-Profiling and Wavefront-Sensing of THz Pulses at the Focus of a Substrate-Lens

We report combined wavefront detection and beam profiling of single-cycle terahertz (THz) pulses. In our system, the electric field is recorded highly resolved in two spatial and one temporal dimension before and after propagation through an optical component. Using this approach, we examine the imaging properties of a hyperhemispherical silicon lens as it is commonly used in THz dipole antennas. We observe an asymmetric spatiotemporal field dynamic in the focus, which can be attributed to distortion of the incident wavefront in combination with the image properties of the lens. Diffraction on the lens aperture influences the spectral beam profile at the focus. The frequency dependence of the Airy pattern indicates a rapidly degrading Strehl ratio with increasing frequency.

Seismic data processing with curvelets: a multiscale and nonlinear approach.

In this abstract, we present a nonlinear curvelet-based sparsitypromoting formulation of a seismic processing flow, consisting of the following steps: seismic data regularization and the restoration of migration amplitudes. We show that the curvelet’s wavefront detection capability and invariance under the migration-demigration operator lead to a formulation that is stable under noise and missing data.

Detection of wave fronts in the Indian Ocean from geostationary sunglint satellite imagery

We demonstrate the potential of monitoring coherent wave fronts on the tropical ocean surface using an advanced detection algorithm applied to visible sunglint‐affected imagery from geostationary satellites. Data from MeteoSat are processed with the advanced analysis technique to reveal transient wave activity near and to the west of the Mascarene Ridge of the western Indian Ocean. The technique is based on a wavelet‐based singularity analysis which enhances the subtle but highly coherent wave patterns in the meteorological satellite data. It is likely that the patterns represent internal ocean waves, a pathway to ocean mixing and climate. The prospect for using this detection algorithm in greatly expanded satellite global surveys of wave activity is outlined.

Adaptive Optics for the control of laser beam in gravitational wave interferometers

In this paper we present the experimental results of the application of Adaptive Optics (AO) technique to control the laser beam in gravitational wave interferometer. In particular, we focus our attention on two specific applications. The first one is the reduction of laser geometrical aberrations by using an AO system based on interferometric wavefront detection. The second application is the use of deformable mirrors for the generation of the non-Gaussian flat laser beams proposed for the reduction of thermoelastic noise in future detectors.

Application of eigenmode in the adaptive optics system based on a micromachined membrane deformable mirror

The construction process and characteristics of a deformable mirror eigenmode are introduced. The eigenmode of a 37-element micromachined membrane deformable mirror (MMDM) from OKO, Ltd. is analyzed. The Gaussian-Seidel low-order aberrations are fitted with eigenmodes as basic functions. An experimental adaptive optics (AO) system is constructed with the MMDM as the wavefront corrector, a deformable mirror eigenmode as the wavefront control algorithm, and a Shack-Hartmann wavefront sensor as the wavefront detector. The experimental results demonstrate that the deformable mirror eigenmode can act as the wavefront control algorithm for the AO system based on the MMDM.

Highly sensitive wave-front sensor with a non-zero-order phase plate

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order pi phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems.

Adaptive acoustic imaging using aberration correction in difficult materials

This paper describes the key technological developments in the design of an adaptive optical scanning acoustic microscope. Adaption is a key technological advance because it enables the microscope to correct for the deleterious effects of the material microstructure, and gain robust instrument performance on a wide range of samples. The two important requirements for the instrument are a multi-channel acoustic wavefront detector to measure the aberration in the acoustic wavefront, and a highly adaptive acoustic source to correct for the effects of aberration. As well as describing the novel aspects of the instrument that allow it to adapt, we present experimental surface acoustic wave images acquired by the instrument that indicate the degree of performance improvement that can be achieved when adaption is used to correct for material aberration.

Method for measuring small optical absorption coefficients with use of a Shack-Hartmann wave-front detector.

We present a method for measuring absorption at the 1 x 10(-5) cm(-1) level in high-quality optical materials. Using a Shack-Hartmann wave-front detector, thermal lensing in these materials may be measured. Then, the absorption coefficient may be estimated by fitting the observed deformation to a thermal lensing model based on the temperature dependences of the refractive index and the thermal expansion coefficient. For a particular sample of fused silica, the absorption coefficient was determined to be 1.8 +/- 0.4 x 10(-5) cm(-1). Obtaining this result requires a resolution in the optical path length better than +/- 0.1 nm.

Characteristics of a Guided-Wave Displacement Sensor Based on Wavefront Detection

The characteristics of a guided-wave displacement sensor based on the wavefront detection are obtained. The displacement is measured by detecting the wavefront gradient of the light reflected from the measured object. The wavefront gradient is determined using the mode interference of the even and odd modes in the double-mode waveguide which is fabricated of silica glass on a Si substrate. The measuring range is 3 µm and the resolution is determined to be less than 1 nm. The object tilting dependence and the stability of the sensor are also measured. Furthermore, sample surfaces are observed and very fine images are obtained using this sensor. The optical system is very simple and the sensor is very compact, hence it will be useful as a built-in component for various kinds of industrial equipment.

Highly sensitive method of shock wave front detection in polymers based on the total internal reflection of light

Highly sensitive method of shock wave front detection in polymers based on the total internal reflection of light

Interferogram analysis based on the data-dependent systems method for nanometrology applications

A spatial method of wave-front phase detection from an interferogram is presented. The method uses data-dependent systems methodology, an approach that extends and improves the way the stochastic autoregressive moving average models are obtained and interpreted. Its application to interference data addresses the fundamental problem of recovering the self-coherence function commonly used to retrieve the wave-front phase. The self-coherence function is efficiently computed by means of a complex autoregressive model and is used for surface reconstruction. The method is shown to be robust and suitable for surface testing. The correspondence of the data-dependent systems methodology and its physical meaning as related to the classical interferometry are presented. The theoretical development is illustrated by experimental implementation, with the results obtained from one- and two-dimensional interferometric fringe analysis of a computer hard disk.

Data-dependent-systems and Fourier-transform methods for single-interferogram analysis

Results of wave-front phase detection obtained from a spatial method based on data-dependent-systems (DDS) methodology are compared with those obtained from the Fourier-transform method. DDS is a novel approach that extends and improves the way the stochastic autoregressive moving-average models are obtained and interpreted. The methodology is robust to noise influence and insensitive to the errors commonly associated with the Fourier transform. Both the Fourier-transform and the DDS methods use one interference pattern, and both offer means for filtering out disturbances such as noise and background variations. We present a brief review of the two methods to compare them theoretically, and then we describe their experimental implementation. The methods were applied to the same interferometric data sets, and the results are presented and compared to discuss relative advantages and disadvantages. In particular, it is shown that the DDS method preserves the detailed surface texture because a convolution of the component that represents the surface dynamic aspect with the component that corresponds to the independent and dynamic-free aspect is able to recover the original details. In contrast the Fourier-transform method smooths such details to an extent that depends on the subjective choice of filters.

Extrasolar planet detection

This paper discusses the concept of extrasolar planet detection using a large-aperture infrared imaging telescope. Coronagraphic stellar apodization techniques are less efficient at infrared wavelengths compared to the visible, as a result of practical limitations on aperture dimensions, thus necessitating additional starlight suppression to make planet detection feasible in this spectral domain. We have been investigating the use of rotational shearing interferometry to provide up to three orders of magnitude of starlight suppression over broad spectral bandwidths. We present a theoretical analysis of the system performance requirements needed to make this a viable instrument for planet detection, including specifications on the interferometer design and telescope aperture characteristics. The concept of using rotational shearing interferometry as a wavefront error detector, thus providing a signal that can be used to adaptively correct the wavefront, will be discussed. We also present the status of laboratory studies of on-axis source suppression using a recently constructed rotational shearing interferometer that currently operates in the visible.

Heterodyne detection of weak optical wavefronts burried in a photorefractive fanning noise

Weak signals, initially burried in the beam fanning noise of photorefractive amplifiers can be efficiently detected by combining the temporal filtering properties of coherent receivers with a spatial averaging over the random noise distribution that occurs from photorefractive effects. This is demonstrated by modulating in time the signal or the pump beam. Theoretical and experimental investigations using photorefractive BaTiO 3 in four different configurations are reported and compared.

Heterodyne Doppler 1-μm lidar measurement of reduced effective telescope aperture due to atmospheric turbulence

We performed an experimental study on the effect of atmospheric turbulence on heterodyne and direct detection lidar at 1 microm, employing a pulsed Nd:YAG bistatic focused beam lidar that permitted simultaneous heterodyne and direct detection of the same lidar returns. The average carrier-to-noise ratio and statistical fluctuation level in the lidar return signals were measured in various experimental and atmospheric conditions. The results showed that atmospheric turbulence could reduce the effective receiver telescope diameter of the l-microm heterodyne lidar to <5cm at a relatively short range of approximately 450 m near the ground. The observed effective telescope aperture and heterodyne detection efficiency varied during the day as the atmospheric turbulence level changed. At this time, we are not able to compare our experimental lidar data to a rigorous atmospheric turbulence and lidar detection theory which includes independently variable transmitter, receiver, and detector geometry. It is interesting to note, however, that the observed limitation of the effective receiver aperture was similar in functional form with those predictions based on the heterodyne wavefront detection theory by D. L. Fried [Proc. IEEE 55, 57-67 (1967)] and the heterodyne lidar detection theory for a fixed monostatic system by S. F. Clifford and S. Wandzura [Appl. Opt. 20, 514-516 (1981)]. We have also applied such an effective receiver aperture limitation to predict the system performance for a heterodyne Ho lidar operating at 2 microm.

Two-wave mixing with time-modulated signal in Bi12SiO20 theory and application to homodyne wave-front detection

We theoretically analyze a two-wave mixing interaction in photorefractive Bi12SiO20 crystals in which the amplitude of the signal beam is time modulated at high frequency. Calculations of the photoinduced space-charge field are derived for a sinusoidal modulation of the input signal. Due to the time-integrating properties of the nonlinear crystal, the transmitted signal exhibits a differential gain when the modulating frequency is much greater than the inverse of the material response time. Application to coherent homodyne detection of wave fronts carrying spatial and temporal information is also presented.

Some algorithms for data analysis in interference wavefront detectors

Several comments may be made. Two method of organizing interference-pattern scanning may be organized. The first entails invoking the points of a scan from a dense Cartesian raster stored in a computer memory, while for each subsequent point the given scan-selection condition must be verified. The second involves controlling the scanning aperture, when the satisfaction of the selection condition is verified by a servosystem, changing the scanning line as necessary. No excess information is stored in the computer here. The comparative characteristics of these two versions remain to be elucidated. Some difficulties are involved in obtaining a priori information on the position of the extremal points of the phase and the form of the extremum. These complications are not specific to any specific recovery algorithm but are characteristic for interferometry in general. It is evidently necessary to count on the possibility of introducing a linear phase shift between the reference and object waves, which is necessary to eliminate extrema. In addition, it is possible to construct a flexible mirror such that the phase extrema will coincide with the points of force application.