Development of a line-scan CCD-based fringe tracker for optical interferometry

Traditional high-precision optical techniques, such as interferometry, are in ever-greater demand for noncontrolled environments. This is the case for the UPC-ZEBRA, a large-aperture interferometer that was built to measure vertical discontinuities (i.e., piston errors) in segmented mirrors. The large mechanical systems used to drive the interferometer to the different measurement positions generate perturbations that are highly incompatible with the expected piston measurements on the nanometer scale. We introduce a new system based on a line-scan CCD to track interference fringes. The error signal obtained from this fringe tracker has been used in a closed-loop control system to actively stabilize the interferometer. The perturbation has been attenuated by a factor of 1/200.     

Contrast enhancement for electronic speckle pattern interferometry fringes by the differential equation enhancement method

Electronic speckle pattern interferometry fringe patterns usually have poor contrast so it is important to enhance fringe contrast for the extraction of phase from a single fringe pattern. We present new enhancement methods based on differential equations (called DE enhancement methods) to electronic speckle pattern interferometry fringes. The DE enhancement methods transform the image processing to solve differential equations. With the proposed methods, the visibility of the correlation speckle fringe patterns can be improved significantly. We tested the proposed methods on computer-simulated speckle correlation fringes and experimentally obtained fringes, and we compared the new method with other contrast enhancement techniques. The experimental results illustrate the performance of this approach.     

Reflective surfaces for panoramic imaging

A family of reflective surfaces is presented that, when imaged by a camera, can capture a global view of the visual environment. By using these surfaces in conjunction with conventional imaging devices, it is possible to produce fields of view in excess of 180 degrees that are not affected by the distortions and aberrations found in refractive wide-angle imaging devices. By solving a differential equation expressing the camera viewing angle as a function of the angle of incidence on a reflective surface, a family of appropriate surfaces has been derived. The surfaces preserve a linear relationship between the angle of incidence of light onto the surface and the angle of reflection onto the imaging device, as does a normal mirror. However, the gradient of this linear relationship can be varied as desired to produce a larger or smaller field of view. The resulting family of surfaces has a number of applications in surveillance and machine vision.     

Mueller matrix error correction for a fringe-free interferometry system

We present an automated surface profiling system based on a shearing interferometer, in which precise measurement of the polarization states eliminates fringe ambiguity. A full error correction based on Mueller matrices allows comparatively inaccurate but rapidly switchable liquid-crystal wave plates to be used, enabling unambiguous profile information to be obtained in real time.     

Two-photon interferometry for high-resolution imaging

This paper discusses the advantages of using non-classical states of light for two aspects of optical imaging: the creation of microscopic images on photosensitive substrates, which constitutes the foundation for optical lithography, and the imaging of microscopic objects. In both cases, the classical resolution limit given by the Rayleigh criterion is approximately half of the optical wavelength. It has been shown, however, that by using multi-photon quantum states of the light field, and a multi-photon sensitive material or detector, this limit can be surpassed. A rigorous quantum mechanical treatment of this problem is given, some particularly widespread misconceptions are addressed, and turning quantum imaging into a practical technology is discussed.     

Tilt-compensating algorithm for phase-shift interferometry

A self-calibrating algorithm for phase-shift interferometry is described that is able to cancel the effect of accidental relative tilts that may occur during phase stepping. The algorithm is able to retrieve both the phase steps and the tilts that accompany them. Only three phase-shifted interferograms are needed, and no other information about the intentional phase shifts or possible tilts has to be supplied. This purpose is achieved by division of the interferogram space into blocks on which a previously reported self-calibrating algorithm is applied and the actual values of the local phase shifts are calculated. The information thus obtained is used for extracting the global shift and tilt values. Further improvement in the results is achieved by means of a fitting routine.     

Achromatic phase-shifting for white-light interferometry

The geometric (Pancharatnam) phase provides a method of introducing a variable phase shift that is almost independent of the wavelength and opens up new possibilities in broadband interferometry.     

Phase-step calibration for phase-stepped interferometry

A novel method to set the proper phase steps, as used in phase-stepped interferometry, is presented. It is indicated how and when this method can be used. With only two images one can deduce the relative phase step between them by calculating the correlation between the two images. The error of the proposed method is shown to be smaller than 0.1%.     

Scanning delay line with a rotating-parallelogram prism for low-coherence interferometry

We describe a fast scanning optical delay line for low-coherence interferometry that has good linearity, a high duty cycle, and a continuously adjustable scan range. The delay line consists of a rotating-parallelogram prism with the rotation axis tilted with respect to the incident beam and two motionless mirrors. The delay line is well suited for nearly simultaneous distance measurements at two different depths, which is useful for making absolute and differential distance measurements.     

Phase-shifting interferometry by a covariance-based method

A novel generalized approach to phase-shifting interferometry in which phase distribution in an interferogram is evaluated in the presence of nonsinusoidal waveforms and piezoactuator device miscalibration is proposed. The approach is based on the underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets. The advantage of the proposed method lies in its ability to identify arbitrary phase-step values pixelwise from an interference signal buried in noise. The robustness of the proposed method is investigated by addition of white Gaussian noise during the simulations.     

Sub-Nyquist interferometry using a computer-stored reference

Abstract

In the testing of deep aspheric wavefronts using the phase-shifting technique a CCD video camera and a digital computer is limited by the so-called Nyquist frequency. The Nyquist frequency limits the maximum wavefront slope that can be measured over the CCD array to π radians per pixel. A wavefront containing spatial frequencies beyond this limit gives a sub-sampled or aliased interferogram. If the wavefront under test is assumed to be smooth up to its first or second derivative, then it is possible to recover the deep aspheric wavefront. Here we present a new and simple technique to recover a deep aspheric wavefront under test whenever a close estimation of the wavefront being tested is available.     

Adaptive interferometry of protein on a BioCD

Adaptive spinning-disk interferometry is capable of measuring surface profiles of a thin biolayer with subnanometer longitudinal resolution. High-speed phase modulation in the signal beam arises from the moving surface height profile on the spinning disk and is detected as a homodyne signal via dynamic two-wave mixing. A photorefractive quantum-well device performs as an adaptive mixer that compensates disk wobble and vibration while it phase-locks the signal and reference waves in the phase quadrature condition (pi/2 relative phase between the signal and local oscillator). We performed biosensing of immobilized monolayers of antibodies on the disk in both transmission and reflection detection modes. Single- and dual-analyte adaptive spinning-disk immunoassays were demonstrated with good specificity and without observable cross-reactivity. Reflection-mode detection enhances the biosensing sensitivity to one-twentieth of a protein monolayer, creates a topographic map of the protein layer, and can differentiate monolayers of different species by their effective optical thicknesses.     

Design of a panoramic annular lens with a long focal length

A new method to improve the design of the panoramic annular lens (PAL) optical system with long focus is introduced. Cemented lenses are used in a PAL block to improve the design freedom. A multilayer diffractive optical element (MDOE) is used in relay optics to simplify the structure of the system and to increase diffractive efficiency of the design spectral range. The diffractive efficiency of MDOE in a wide spectral range is investigated theoretically. A seven piece PAL system with a total effective focal length of 10.8 mm is realized, and the diffractive efficiency of the whole design wavelength is above 99.3%. A PAL system with all spherical surfaces is described as a comparison.     

A quantum Rosetta stone for interferometry

Heisenberg-limited measurement protocols can be used to gain an increase in measurement precision over classical protocols. Such measurements can be implemented using, for example, optical Mach—Zehnder interferometers and Ramsey spectroscopes. We address the formal equivalence between the Mach—Zehnder interferometer, the Ramsey spectroscope and a generic quantum logic circuit. Based on this equivalence we introduce the 'quantum Rosetta stone', and we describe a projective-measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity. The Rosetta stone then tells us that the same method should work in atom spectroscopy.     

Focus retrocollimated interferometry for focal-length measurements

Focus retrocollimated interferometry is developed for the measurement of focal lengths of optical lenses and systems, and achievable accuracy is discussed. It is shown that this method can be used to measure both short and long focal lengths simply and with high accuracy.     

Semiconductor line source for low-coherence interferometry

The suitability for low-coherence interferometry of a high-power, semiconductor laser line source operated at a forward bias current below threshold is demonstrated. Measurements of the important characteristics of the source are presented. For example, the source produces an output power of 1.3 mW and a spatially uniform coherence length of 16 mum at a bias current of 86% of threshold (250 mA) at 20 degrees C. The usefulness of the source is verified by measurement of the line profile of a contact lens.