Reference Mirror Research Articles

Interference microscope objectives for wide-field areal surface topography measurements

We propose a type of interference objective that extends the range of application for flexible microscope platforms to larger fields of view. The objective comprises a beamsplitter plate and a partially transparent reference mirror arranged coaxially with the objective lens system. The coaxial plates are slightly tilted to direct unwanted reflections outside of the imaging pupil aperture, providing high fringe contrast with spatially extended white-light illumination. Examples include a turret-mountable 1.4× magnification objective parfocal with high-magnification objectives up to 100× and a dovetail mount 0.5× objective with a 34×34 mm field. This design is a practical alternative to the classical Michelson and Mirau type objectives for low magnifications.

Compact lensless digital holographic microscopy using a curved mirror for an enlarged working distance.

Digital holographic microscopy (DHM) has a wide range of applications from the analysis of microelectronic mechanical systems (MEMS) to the measurement of cells. We intend on making the system more compact to improve the portability of the device. A concave mirror has been presented to be used in a lensless DHM system to effectively enlarge the working distance and at the same time maintain the compact size of the whole system. A theoretical analysis of the phase compensation between the object wave and the wave reflected from curved reference mirrors is given. Experimental demonstrations of the curved reference mirrors used in the DHM system have been obtained to support our idea. This would change the overall size and adaptability of the DHM system and provide a better understanding of the effects of phase reflected off a curved mirror.

Total measurement of geometric errors of a three-axis machine tool by developing a hybrid technique

A hybrid measurement technique using a five-DOF measuring system and laser interferometer is suggested for all geometric errors of a three-axis machine tool. All geometric errors are defined in a single coordinate system, by eliminating the effect of Abbe’s offsets, for accurate measurement. The five-DOF measurement comprises five capacitive sensors and an L-type reference mirror. The system measures three PIGEs (position independent geometric errors) and five PDGEs (position dependent geometric errors) for each axis. The 18 geometric errors of the machine tool are measured using the results from two experiments (XY and YZ-planes), and the homogeneous transform is used to identify the geometric errors in a single coordinate system, eliminating the effects of installation errors such as mirror misalignment. A laser interferometer is used to measure three PDGEs (one linear displacement error and two straightness errors) for each axis. The two straightness errors are used to estimate the optimal Abbe’s offsets (for the X, Y and Zaxes) between the two measuring coordinate systems, and the linear displacement of each axis is calculated, minimizing the effect of Abbe’s offsets. Through this analytical approach, all geometric errors are expressed for a single coordinate system. The suggested measurement technique can therefore be used to investigate all geometric errors of a three-axis machining tool.

Development of compact three-degrees-of-freedom compensation system for geometric errors of an ultra-precision linear axis

We report a compensation system for geometric errors of a linear axis to achieve the ultra-precision positioning. The system was miniaturized by integrating the drive and measuring components. A novel joint with three DOFs based on a flexure hinge was developed to obtain the ultra-precision positioning. The drive component, which was adapted to the parallel mechanism, had a high structural stiffness and rapid response characteristics. The rotational stiffness of the joint was calculated and the mode shapes were analyzed to verify the feasibility of three-DOF motion. The measurement component consisted of capacitive sensors and a reference mirror to measure the three geometric errors of the linear axis. In addition, the optimal position between the reference coordinate system and a sensor was determined to minimize the standard uncertainties of the measured errors. The compensation system was fabricated and evaluated experimentally. A compensation algorithm based on a recursive technique was developed to improve the positioning accuracy of the system. The geometric errors of the linear axis were measured and compensated for, and a marked improvement was observed compared to the case with no error compensation. The peak-to-valley error of the translational and rotational errors were reduced by 92% and 98%, respectively.

Laser-ranging long-baseline differential atom interferometers for space

High-sensitivity differential atom interferometers (AIs) are promising for precision measurements in science frontiers in space, including gravity-field mapping for Earth science studies and gravitational wave detection. Difficulties associated with implementing long-baseline differential AIs have previously included the need for a high optical power, large differential Doppler shifts, and narrow dynamic range. We propose a configuration of twin AIs connected by a laser-ranging interferometer (LRI-AI) to provide precise information of the displacements between the two AI reference mirrors and also to phase-lock the two independent interferometer lasers over long distances, thereby drastically improving the practical feasibility of long-baseline differential AI measurements. We show that a properly implemented LRI-AI can achieve equivalent functionality to the conventional differential AI measurement configuration.

A closed-loop phase-locked interferometer for wide bandwidth position sensing.

This article describes a position sensitive interferometer with closed-loop control of the reference mirror. A calibrated nanopositioner is used to lock the interferometer phase to the most sensitive point in the interferogram. In this configuration, large low-frequency movements of the sensor mirror can be detected from the control signal applied to the nanopositioner and high-frequency short-range signals can be measured directly from the photodiode. It is demonstrated that these two signals are complementary and can be summed to find the total displacement. The resulting interferometer has a number of desirable characteristics: it is optically simple, does not require polarization or modulation to detect the direction of motion, does not require fringe-counting or interpolation electronics, and has a bandwidth equal to that of the photodiode. Experimental results demonstrate the frequency response analysis of a high-speed positioning stage. The proposed instrument is ideal for measuring the frequency response of nanopositioners, electro-optical components, MEMs devices, ultrasonic devices, and sensors such as surface acoustic wave detectors.

Topography of nanometric thin films with three-wavelength digital interferometry

This paper discusses a method to measure the thickness of thin layers deposited on a reflective substrate. An interferometer with three wavelengths produces color interferences. A color sensor records the tint that is produced. The color interferences are approximated by a model based on the measurement of the laser intensities obtained with the reference mirror only. An iterative process leads to unambiguous algorithmic convergence and high accuracy thickness measurement. This method is simple, robust, compact, and single shot. The method does not need angular scanning over the field of measurement (about 75 mm2). The measurement on the surface yields a histogram of the thickness distribution and there is no requirement for any reference points (e.g., no need to make a groove or a walk on the layer). A thickness measurement performance of 50 nm was demonstrated for homogeneous polymer films deposited on a silicon wafer. The setup and digital image processing are discussed.

Iterative optimization calibration method for stereo deflectometry.

An accurate system calibration method is presented in this paper to calibrate stereo deflectometry. A corresponding iterative optimization algorithm is also proposed to improve the system calibration accuracy. This merges CCD parameters and geometrical relation between CCDs and the LCD into one cost function. In this calibration technique, an optical flat acts as a reference mirror and simultaneously reflect sinusoidal fringe patterns into the two CCDs. The normal vector of the reference mirror is used as an intermediate variable to implement this iterative optimization algorithm until the root mean square of the reprojection errors converge to a minimum. The experiment demonstrates that this method can optimize all the calibration parameters and can effectively reduce reprojection error, which correspondingly improves the final reconstruction accuracy.

Dichroic spectrally-resolved interferometry to overcome the measuring range limit

In this investigation, a simple method to eliminate the dead zone without the minimum measurable distance and extend the measurable range of spectrally resolved interferometry (SRI) twice based on the bandwidth separation by a dichroic beam splitter (DBS) is proposed. The main advantage of this dichroic SRI is that it can be simply implemented with a dichroic beam splitter and another reference mirror from the typical SRI. Feasibility experiments were performed to verify the principle of the dichroic SRI and the result confirmed the effectiveness of this method as the extended measuring range. Some practical error sources are considered and the alternative solutions are also discussed.

Dark-field full-field optical coherence tomography.

Full-field optical coherence tomography (FF-OCT) provides en face images from deep in the tissue with high spatial resolution. Specular reflections, however, may reduce image contrast as it can be much stronger than the backscattered signal from a specimen. To this end, we demonstrate dark-field FF-OCT (d-FF-OCT) that can block specular reflections by the help of an opaque disk in the pupil-conjugated plane. The reference mirror is replaced by a blazed grating, which eliminates a walk-off between the sample and the reference beams on a camera that otherwise limits the imaging field-of-view (FOV). We show that d-FF-OCT can suppress specular reflections efficiently from the glass-specimen interface by at least two orders of magnitude and yield higher contrast images compared to the conventional FF-OCT.

The Approach of Compensation of Air Refractive Index in Thermal Expansion Coefficients Measurement Based on Laser Feedback Interferometry**Supported by the National Natural Science Foundation of China under Grant No F050306.

We present the thermal expansion coefficient (TEC) measurement technology of compensating for the effect of variations in the refractive index based on a Nd:YAG laser feedback system, the beam frequency is shifted by a pair of acousto-optic modulators and then the heterodyne phase measurement technique is used. The sample measured is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams hit perpendicularly and coaxially on each surface of the sample. The reference beams hit on the reference mirror and the high-reflectivity mirror, respectively. By the heterodyne configuration and computing, the influences of the vibration, distortion of the sample supporter and the effect of variations in the refractive index are measured and largely minimized. For validation, the TECs of aluminum samples are determined in the temperature range of 298–748 K, confirming not only the precision within 5 × 10−7 K−1 and the accuracy within 0.4% from 298 K to 448 K but also the high sensitivity non-contact measurement of the lower reflectivity surface induced by the sample oxidization from 448 K to 748 K.

Automated working distance adjustment enables optical coherence tomography of the human larynx in awake patients.

Optical coherence tomography (OCT) provides structural information of laryngeal tissue which is comparable to histopathological analysis of biopsies taken under general anesthesia. In awake patients, movements impede clinically useful OCT acquisition. Therefore, an automatic compensation of movements was implemented into a swept source OCT-laryngoscope. Video and OCT beam path were combined in one tube of 10-mm diameter. Segmented OCT images served as distance sensor and a feedback control adjusted the working distance between 33 and 70mm by synchronously translating the reference mirror and focusing lens. With this motion compensation, the tissue was properly visible in up to 88% of the acquisition time. During quiet respiration, OCT contrasted epithelium and lamina propria. Mean epithelial thickness was measured to be 109 and [Formula: see text] in female and male, respectively. Furthermore, OCT of mucosal wave movements during phonation enabled estimation of the oscillation frequency and amplitude. Regarding clinical issues, the OCT-laryngoscope with automated working distance adjustment may support the estimation of the depth extent of epithelial lesions and contribute to establish an indication for a biopsy. Moreover, OCT of the vibrating vocal folds provides functional information, possibly giving further insight into mucosal behavior during the vibratory cycle.

Impact of mirror spider legs on imaging quality in Mirau micro-interferometry.

We report the impact on imaging quality of mirror suspensions, referred to as spider legs, used to support the reference mirror in a Mirau micro-interferometer that requires the vertical alignment of lens, mirror, and beamsplitter. Because the light goes from the microlens to the beamsplitter through the mirror plane, the spider legs are a source of diffraction. This impact is studied as a function of different parameters of the spider legs design. Imaging criteria, such as the resolution as well as the symmetry of the imaging system, are determined using the point spread function and the modulation transfer function of the pupil. These imaging criteria are used to determine the optimum radius of curvature, thickness, and number of legs of the spider structure. We show that 3 curved legs give performances, with specific radius of curvature and thickness, similar to a suspension-free mirror.

Hemispherical Reflectance Results of the SolarPACES Reflectance Round Robin

Abstract Mirrors are the first link in the energy-conversion chain from Sun to electricity-delivery in the grid. Shape and solar reflectance are the key-parameters of mirrors, respectively affecting how solar radiation is concentrated around the focus, and how much of the impinging solar power is reflected. In SolarPACES Task III, an expert group is drafting the solar reflectance guidelines; in order to speed up the discussion the SRRR round robin was launched at the beginning of 2013. Identical kits, each one consisting of ten specimens collected from eight cooperating producers, were distributed and measured at six research institutes, acting as evaluators. The kit includes both traditional (glass based) and innovative (first-surface) solar mirrors. The paper only reports on the simplest task among those of SRRR: the solar hemispherical reflectance measurement. Near-specular solar reflectance was also measured and compared but the results are still under investigation and are not part of this paper. The measurements were accomplished according to the guidelines. The differences among the achieved results are within the typical accuracy of spectrophotometers, demonstrating the reliability of the reflectance guidelines. The statistic of the deviations from the true value is analysed separately for each evaluator, and allows us to infer information abut the gauging-status of the adopted reference mirror, as well as the measurement reproducibility.

Ultra-Precision Polishing of N-Bk7 Using an Innovative Self-Propelled Abrasive Fluid Multi-Jet Polishing Tool

As the demand for optical glasses has increased, precision requirements for specific shapes, forms, surface textures, and sizes (miniaturization) have also increased. The standards and surface finishes applied to the reference mirrors used in measuring appliances are crucial. Hence, enhancements in figuring and surface finishing are indispensable to manufacturing industries. In this article, a novel self-propelled multi-jet abrasive fluid polishing technique is proposed for an ultra-precision polishing process in which a blade-less Tesla turbine was used as a prime mover. The turbine was characterized by high swirling velocity at the outlet; therefore, high levels of kinetic energy moving away from the turbine were used as polishing energy. Computational fluid dynamics (CFD) was also used to simulate the flow on the turbine blades. With a newly designed and manufactured polishing tool, the optimal polishing parameters for improving the surface roughness of crown optical glasses (N-BK7) were investigated. Taguchi's experimental approach, an L18 orthogonal array, was employed to obtain the optimal process parameters. An analysis of variance (ANOVA) was also conducted to determine the significant factors. The surface roughness has been improved by approximately 94.44% from (Ra) 0.36 μm to (Ra) 0.02 μm. This study also presents a discussion on the influence of significant factors on improving surface roughness.

Study of non-contact measurement of the thermal expansion coefficients of materials based on laser feedback interferometry.

The noncooperative and ultrahigh sensitive length measurement approach is of great significance to the study of a high-precision thermal expansion coefficient (TEC) determination of materials at a wide temperature range. The novel approach is presented in this paper based on the Nd:YAG microchip laser feedback interferometry with 1064 nm wavelength, the beam frequency of which is shifted by a pair of acousto-optic modulators and then the heterodyne phase measurement technique is used. The sample is placed in a muffle furnace with two coaxial holes opened on the opposite furnace walls. The measurement beams are perpendicular and coaxial on each surface of the sample, the configuration which can not only achieve the length measurement of sample but also eliminate the influence of the distortion of the sample supporter. The reference beams inject on the reference mirrors which are put as possible as near the holes, respectively, to eliminate the air disturbances and the influence of thermal lens effect out of the furnace chamber. For validation, the thermal expansion coefficients of aluminum and steel 45 samples are measured from room temperature to 748 K, which proved measurement repeatability of TECs is better than 0.6 × 10(-6)(K(-1)) at the range of 298 K-598 K and the high-sensitive non-contact measurement of the low reflectivity surface induced by the oxidization of the samples at the range of 598 K-748 K.

Self-calibrating phase measurement based on diffraction theory and numerical simulation experiments

To achieve a full-aperture, diffraction-limited image, a telescope’s segmented primary mirror must be properly phased. Furthermore, it is crucial to detect the piston errors between individual segments with high accuracy. Based on the diffraction imaging theory, the symmetrically shaped aperture with an arbitrarily positioned entrance pupil would focus at the optical axis with a symmetrical diffraction pattern. By selecting a single mirror as a reference mirror and regarding the diffraction image’s center as the calibration point, a function can be derived that expresses the relationship between the piston error and the distance from the center of the inference image to the calibration point is linearity within one-half wavelength. These theoretical results are shown to be consistent with the results of a numerical simulation. Using this method, not only the piston error, but also the tip–tilt error can be detected. This method is simple and effective; it yields high-accuracy measurements and requires less computation time.

Synchronous scanning of reference mirror and objective lens for high-resolution full-field interferometry

We realized a long-scanning-range and high-resolution interferometry in a time-domain full-field microscopic scheme by adopting a simple configuration. A reference mirror was synchronously scanned with an objective lens, which was installed in a common path, to prevent lateral resolution degradation due to defocus at the mirror. High axial resolution was obtained using a broadband supercontinuum (SC) generated by a 1.55 µm pump. The SC was generated by propagating a femtosecond pulse at 1.55 µm through a highly nonlinear dispersion shifted fiber with a small dispersion slope. We designed and constructed an interferometer carefully to utilize the entire bandwidth. The broad bandwidth of the interferometer achieved an axial resolution of 2.50 µm in air. The synchronous scanning maintained a lateral resolution longer than 1 mm. The system successfully yielded a cross-sectional image of two layers of scotch tape along the 400-µm-depth and 90-nm-step surface profiles.

Determination of the tangential surface profile of Toroidal beam line mirrors with polarization phase-shifting Twyman–Green interferometer

A new technique for the measurement of the tangential surface profile of Toroidal mirrors (TMs) used in synchrotron radiation beam lines is proposed. A cylindrical lens placed in the collimated input (He–Ne laser) beam of a polarization Twyman–Green interferometer (TGI) forms line foci in the reference and test arms. The effect of the sagittal curvature of the TM is eliminated by adjusting a line focus on the surface of the TM, along the central tangential section. Thus, a toric test wavefront (TTW) with sagittal curvature identical to that of the incident cylindrical wavefront and tangential curvature with slope twice that of the TM, is produced along the reflection direction. The TTW interferes with a reference cylindrical wavefront, generated by retroreflecting the incident cylindrical wavefront from a reference plane mirror in the reference arm of the TGI and having identical curvature in the sagittal direction. Polarization phase-shifting interferometry has been applied to obtain the tangential surface profile of the test TM. Results are compared with other methods. The advantages of the technique are that only a plane reference mirror is needed to generate the reference beam, and the technique is suitable for TMs with long tangential radii of curvature in the kilometer regime.

LED-based digital holographic microscopy with slightly off-axis interferometry

An LED illuminated Linnik-type digital holographic microscope (DHM) for high-quality phase imaging is presented by the adoption of slightly off-axis two-step blind-phase-shifting interferometry (TB-PSI). Slightly off-axis interferometry lowers the requirement on the angle between the object and the reference waves as well as the requirement on the resolving power of the charge-coupled device (CCD) camera. In addition, the apparatus is cost-effective and offers ease of alignment. The phase-shifting DHM is simply implemented by mechanically moving the reference mirror while disposing of a precise phase modulator such as a piezoelectric transducer (PZT). The phase shift between the two interferograms is extracted by Fourier transformation analysis, and then the phase image is reconstructed. The performance of the TB-PSI used in the scheme is analyzed. The phase imaging for nanostructured specimens is conducted, and the results demonstrate the feasibility of the scheme. The phase noise is reduced by 73% when compared to the result obtained with coherent illumination.