Infrared point diffraction interferometer

Directional phase-unwrapping algorithm and phase shift technique on hydrogel

Refractive index microstructures, which can be written by multiphoton absorption with femtosecond lasers, have many applications. Here we present a directional phase-unwrapping algorithm with phase-shifting technique and apply it to the metrology of hydrogel microstructures. A staircase phase-unwrapping algorithm is demonstrated. This fast quality-guided path phase-unwrapping applies well to situations that are geometrically well defined and is quite tolerant of phase noise. To achieve precise very small phase shifts, we also present a slant angle technique on a DC servo stage along with phase shift measurement, allowing us to achieve 6.5 nm step sizes.

Characterization of the pinhole diffraction based on the waveguide effect in a point diffraction interferometer

The nearly ideal spherical wavefront generated by pinhole diffraction is the key factor determining the achievable accuracy in point diffraction interferometers (PDIs), as it is employed as the reference wavefront. A comprehensive characterization of the diffraction of a pinhole at the operating-wavelength scale that is normally adopted in PDI is given. The incident light is coupled into the pinhole, which functions as a cylindrical waveguide, and is diffracted in the end. The field in the pinhole is analyzed based on mode theory and the diffraction wave in the far field is derived from the field equivalence principle. The diffraction wave is characterized by the light transmittance, the polarization, and the wavefront aberration, which are all determined by the properties of the mode in the pinhole. The diameter of the pinhole should not be smaller than 0.6λ to make the transmittance sufficient. With a linearly polarized incident light, the diffraction wave is elliptically polarized, and the wavefront aberration is dominated by the astigmatic component. The method explicitly reveals the physical mechanism of pinhole diffraction. The analytic solutions are fast to compute, easy to analyze, and intuitively show the diffractive properties of the pinhole. The conclusions are significant for insight into the nature of pinhole diffraction and provide theoretical reference for analysis of numerical results and the design of PDI systems.

Complex amplitude reconstruction for dynamic beam quality M2 factor measurement with self-referencing interferometer wavefront sensor

A real-time complex amplitude reconstruction method for determining the dynamic beam quality M² factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M² factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

Measurement of M²-Curve for Asymmetric Beams by Self-Referencing Interferometer Wavefront Sensor

For asymmetric laser beams, the values of beam quality factor Mx2 and My2 are inconsistent if one selects a different coordinate system or measures beam quality with different experimental conditionals, even when analyzing the same beam. To overcome this non-uniqueness, a new beam quality characterization method named as M²-curve is developed. The M²-curve not only contains the beam quality factor Mx2 and My2 in the x-direction and y-direction, respectively; but also introduces a curve of Mxα2 versus rotation angle α of coordinate axis. Moreover, we also present a real-time measurement method to demonstrate beam propagation factor M²-curve with a modified self-referencing Mach-Zehnder interferometer based-wavefront sensor (henceforth SRI-WFS). The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment in multimode beams. The experimental results showed that the proposed measurement method is simple, fast, and a single-shot measurement procedure without movable parts.

Interferometric Local Measurements of High-Order Aberrations in Progressive Addition Lenses

PURPOSE

The main goal of this work is to show the principles, design, and performance of a modified point diffraction interferometer (PDI) for evaluating the local higher-order aberrations of progressive addition lenses (PALs). Because aberrations have different impacts in visual perception, we propose a device to provide a customized solution with the best permissible amounts and combinations of aberrations for improving a subject's vision.

METHODS

A PDI has been adapted to measure local high-order aberrations in PALs.

RESULTS

High-order aberrations in three different PALs within four relevant circular regions of interest (ROIs) with a radius ranging from 0.4 to 2.4 mm were measured with an accuracy of λ/10 within the ROI using the tailored PDI. The interferometer also allows for easily choosing the position and number of the ROIs.

CONCLUSIONS

The interferometric device is compact, robust, and accurate. The operational principle is very simple, and it provides the local high-order aberrations directly without adding additional parts to the interferometer. As expected, the amount of high-order aberrations depends on the chosen ROI of the PAL; the corridor is the more critical region. We found, in accordance with the literature, that, in the corridor, second- and third-order aberrations are dominant and spherical aberration is negligible.

Self-calibrating common-path interferometry

A quantitative phase measuring technique is presented that estimates the object phase from a series of phase shifted interferograms that are obtained in a common-path configuration with unknown phase shifts. The derived random phase shifting algorithm for common-path interferometers is based on the Generalized Phase Contrast theory [pl. Opt.40(2), 268 (2001)10.1063/1.1404846], which accounts for the particular image formation and includes effects that are not present in two-beam interferometry. It is shown experimentally that this technique can be used within common-path configurations employing nonlinear liquid crystal materials as self-induced phase filters for quantitative phase imaging without the need of phase shift calibrations. The advantages of such liquid crystal elements compared to spatial light modulator based solutions are given by the cost-effectiveness, self-alignment, and the generation of diminutive dimensions of the phase filter size, giving unique performance advantages.

Measurement of spherical and cylindrical power in ophthalmic lenses based in the change of lateral amplification

In this article, we present a new technique to measure spherical and cylindrical power in ophthalmic lenses. This method is based in the change of lateral amplification produced by an optical system when introducing an ophthalmic lens. Ophthalmic lens power is calculated by considering the change in image size from a reference object and its own image seen through the ophthalmic lens. Mathematical analysis is presented along with the experimental setup and the obtained results. Several algorithms were applied to the obtained results as a method to compensate the error in order to fit into ISO 8598 specifications.

Circular common-path point diffraction interferometer

A simple and compact point-diffraction interferometer with circular common-path geometry configuration is developed. The interferometer is constructed by a beam-splitter, two reflection mirrors, and a telescope system composed by two lenses. The signal and reference waves travel along the same path. Furthermore, an opaque mask containing a reference pinhole and a test object holder or test window is positioned in the common focal plane of the telescope system. The object wave is divided into two beams that take opposite paths along the interferometer. The reference wave is filtered by the reference pinhole, while the signal wave is transmitted through the object holder. The reference and signal waves are combined again in the beam-splitter and their interference is imaged in the CCD. The new design is compact, vibration insensitive, and suitable for the measurement of moving objects or dynamic processes.

Optical pressure sensor based on the combined system of a variable liquid lens and a point diffraction interferometer

We propose an experimental efficient optical pressure sensor based on a variable liquid lens and a modified point diffraction interferometer. The working principle of the sensor is based on the fact that a variation in pressure induces a change in lens curvature and hence in its focal length, which can be tracked and measured with the interferometer. The pressure is then measured by recording and processing the interferometric images. The sensor in this proposal can change its dynamic range by the simple axial movement of one of the components of the optical system. In this work we show the performance of the system within three working ranges: from 0 to 1 kPa with accuracy of approximately 0.01 kPa, from 0 to 7 kPa with 0.05 kPa accuracy, and from 0 to 30 kPa with 0.3 kPa accuracy.

Phase in nanooptics

Quantitative phase measurements in imaging, microscopy, and nanooptics provide information not carried in amplitude measurements alone. In this issue of ACS Nano, Honigstein et al. present a new method in phase measurement. In this Perspective, we comment on this work and more broadly on the emerging role of phase and phase measurements in nanooptics.

Relationship between wave aberrations and histological features in ex vivo porcine crystalline lenses

Wave aberrations of isolated ex vivo porcine crystalline lenses were measured by using a point-diffraction interferometer. This method allowed us to gain greater insight into the detailed aberration structure of eye lenses showing systematic presence of some dominant aberrations. In order of significance, astigmatism together with spherical aberration, coma, and trefoil are the main aberrations present in all lenses. We found a high correlation between the axis of both astigmatism and trefoil with the Y-shaped suture planes of the lens, revealing a subtle relationship between the induced aberrations and the histological features.

Wavefront measurements of phase plates combining a point-diffraction interferometer and a Hartmann-Shack sensor

A dual setup composed of a point diffraction interferometer (PDI) and a Hartmann-Shack (HS) wavefront sensor was built to compare the estimates of wavefront aberrations provided by the two different and complementary techniques when applied to different phase plates. Results show that under the same experimental and fitting conditions both techniques provide similar information concerning the wavefront aberration map. When taking into account all Zernike terms up to 6th order, the maximum difference in root-mean-square wavefront error was 0.08 microm, and this reduced up to 0.03 microm when excluding lower-order terms. The effects of the pupil size and the order of the Zernike expansion used to reconstruct the wavefront were evaluated. The combination of the two techniques can accurately measure complicated phase profiles, combining the robustness of the HS and the higher resolution and dynamic range of the PDI.

Phase-shifting point-diffraction interferometer developed by using the electro-optic effect in ferroelectric crystals

A novel and simple phase-shifting point-diffraction interferometer using a z-cut lithium niobate wafer is proposed. The pinhole is realized by an optical lithography process, aluminum deposition, and subsequent lift-off on the surface of the wafer. The phase shifting is obtained by inducing the electro-optic effect along the z crystal axis. We demonstrate experimentally the possibility of retrieving an aberrated wavefront.

Modified point diffraction interferometer for inspection and evaluation of ophthalmic components

We demonstrate that a modified point diffraction interferometer can be used to measure the power distribution of different kinds of ophthalmic lenses such as spectacles, rigid and soft contact lenses, progressive lenses, etc. The relationship between the shape of the fringes and the power characteristics of the component being tested is simple and makes the design a very convenient and robust tool for inspection or quality control. Some simulations based on the Fresnel approximation are included.

Optimal phase contrast in common-path interferometry

We have developed an analytical model for the design and optimization of common-path interferometers (CPI's) based on spatial filtering. We describe the mathematical analysis in detail and show how its application to the optimization of a range of different CPI's results in the development of a graphical framework to characterize quantitatively CPI performance. A detailed analytical treatment of the effect of curvature in the synthetic reference wave is undertaken. We show that it is possible to improve the linearity and fringe accuracy of certain standard interferometers by a modification of the Fourier filter, and we propose and analyze a dual CPI system for the unambiguous mapping of phase to intensity over the complete input phase range.

Liquid-crystal point-diffraction interferometer for wave-front measurements

A new instrument, the liquid-crystal point-diffraction interferometer (LCPDI), is developed for the measurement of phase objects. This instrument maintains the compact, robust design of Linnik's point-diffraction interferometer and adds to it a phase-stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave fronts with very high data density and with automated data reduction. We describe the theory and design of the LCPDI. A focus shift was measured with the LCPDI, and the results are compared with theoretical results.

Polarization pinhole interferometer

A polarization pinhole interferometer is based on the principles of pinhole diffraction, a common light path, and the polarization technique in its design. It has many advantages, such as adjustable contrast of the fringes, nondestructive testing, and less sensitivity to environmental factors. The instrument can be used extensively in optical element testing and glue-layer testing. The accuracy of the fringe pattern analysis is controlled by the number of sampled points in the fringes. The analysis results of the closed fringe pattern are given.

Multichannel phase-shifted interferometer

A new real-time interferometer based on diffraction phenomena is discussed. It consists of a point-diffraction interferometer fabricated on a transmission grating. The real-time data-analysis capability is achieved by simultaneously introducing a phase shift (piston) on the three separate channels of diffracted interferograms. Mathematical analysis and preliminary observational results are included.

Optical analysis of laser systems using interferometry

Previous methods of predicting focal spot parameters such as the Strehl ratio and encircled energy of large laser systems like the Los Alamos fusion CO(2) lasers involved the digitization of interference patterns of the optical components and propagation of the complex amplitude and phase of the wave front throughout the system. In the new approach described in this paper, the computational procedure has been extended to produce computer plots of the final emerging wave front. This enables direct comparison with the experimentally produced wave front of the total system and opens the way for optical analysis, design, and possible optimization of laser systems, especially CO(2) laser systems. The computational procedure and the Twyman-Green and Smartt IR interferometers constructed to verify this approach are described. The implications of the results are discussed.

Rough surface interferometry at 10.6 microm

An IR Twyman-Green interferometer is described. It uses a cw CO(2) laser as a light source operating at a 10.6-microm wavelength. Theoretical analysis and experimental measurements of the relationship between the contrast of the interference fringes and the rms roughness of test surfaces are discussed. Interferometric testing results and special alignment methods are shown for rough surface optics.