On-chip digital holographic interferometry for measuring wavefront deformation in transparent samples.

This paper describes on-chip digital holographic interferometry for measuring the wavefront deformation of transparent samples. The interferometer is based on a Mach-Zehnder arrangement with a waveguide in the reference arm, which allows for a compact on-chip arrangement. The method thus exploits the sensitivity of digital holographic interferometry and the advantages of the on-chip approach, which provides high spatial resolution over a large area, simplicity, and compactness of the system. The method's performance is demonstrated by measuring a model glass sample fabricated by depositing SiO2 layers of different thicknesses on a planar glass substrate and visualizing the domain structure in periodically poled lithium niobate. Finally, the results of the measurement made with the on-chip digital holographic interferometer were compared with those made with a conventional Mach-Zehnder type digital holographic interferometer with lens and with a commercial white light interferometer. The comparison of the obtained results indicates that the on-chip digital holographic interferometer provides accuracy comparable to conventional methods while offering the benefits of a large field of view and simplicity.

Multiple wavelength digital holography for freeform shape measurement and lens alignment.

This paper introduces a technique for freeform optical surface measurements using digital holography with multiple discrete wavelengths or wavelength scans. This experimental arrangement, i.e., a Mach-Zehnder holographic profiler, is optimized to achieve maximal theoretical precision and is capable of measuring freeform diffuse surfaces. Moreover, the approach can also be used for diagnostics of precise placement of elements within optical systems.

Compact lensless Fizeau holographic interferometry for imaging domain patterns in ferroelectric single crystals.

Domain patterns in ferroelectric single crystals are physical systems that are fascinating from a theoretical point of view and essential for many applications. A compact lensless method for imaging domain patterns in ferroelectric single crystals based on a digital holographic Fizeau interferometer has been developed. This approach provides a large field-of-view image while maintaining a high spatial resolution. Furthermore, the double-pass approach increases the sensitivity of the measurement. The performance of the lensless digital holographic Fizeau interferometer is demonstrated by imaging the domain pattern in periodically poled lithium niobate. To display the domain patterns in the crystal, we have used an electro-optic phenomenon, which, when an external uniform electric field is applied to the sample, produces a difference in refractive index values in domains with different polarization states of the crystal lattice. Finally, the constructed digital holographic Fizeau interferometer is used to measure the difference in the index of refraction in the antiparallel ferroelectric domains in the external electric field. The lateral resolution of the developed method for ferroelectric domain imaging is discussed.

Subaperture stitching digital holographic microscopy for precise wear volume measurement in tribology.

Digital holographic microscopy (DHM) is an effective method for the evaluation of surface topography. It combines the high lateral resolution of microscopy with the high axial resolution of interferometry. In this paper, DHM with subaperture stitching for tribology is presented. The developed approach allows large surface area inspection by stitching together multiple measurements, which brings a big advantage to the evaluation of tribological tests such as a tribological track on a thin layer. The whole track measurement provides additional parameters, which can offer more information on the result of the tribological test than the conventional four-profile measurement by a contact profilometer.

Aspheric surface measurement by absolute wavelength scanning interferometry with model-based retrace error correction.

This paper presents a non-nulling absolute interferometric method for fast and full-area measurement of aspheric surfaces without the necessity of any mechanical movement. Several single frequency laser diodes with some degree of laser tunability are used to achieve an absolute interferometric measurement. The virtual interconnection of three different wavelengths makes it possible to accurately measure the geometrical path difference between the measured aspheric surface and the reference Fizeau surface independently for each pixel of the camera sensor. It is thus possible to measure even in undersampled areas of the high fringe density interferogram. After measuring the geometrical path difference, the retrace error associated with the non-nulling mode of the interferometer is compensated for using a calibrated numerical model (numerical twin) of the interferometer. A height map representing the normal deviation of the aspheric surface from its nominal shape is obtained. The principle of absolute interferometric measurement and numerical error compensation are described in this paper. The method was experimentally verified by measuring an aspheric surface with a measurement uncertainty of λ/20, and the results were in good agreement with the results of a single-point scanning interferometer.

Absolute wavelength scanning interferometry for measuring the thickness of optical elements.

A technique for measurement of the thickness of optical elements using absolute wavelength scanning interferometry is presented in this paper. To achieve high-grade optical components and systems, the thickness of both planar and non-planar optical components must be measured with an accuracy of a few micrometers. The proposed technique is based on the Fizeau interferometer and interconnects data from three different tunable laser diodes yielding a long effective wavelength range and thus low measurement uncertainty. The uncertainty of the central thickness measurement ranges from hundreds of nanometers to a few microns. The method allows to measure the thickness of both flat optical elements as well as lenses with curved surfaces. Moreover, the areal information provided by the interferometry and its high angle sensitivity help to quickly and precisely align the measured component and reduce misalignment errors. The results of thickness measurements have been validated and cross-tested with other techniques. In addition to the thickness, the technique provides some additional information (wedge, surface form error) in the case of flat samples and can be easily and quickly modified (mounting of a Fizeau transmission sphere) to measure other essential parameters of optical elements. Thus, this one approach can replace many single-purpose measuring devices while maintaining high accuracy.

Characterization of Supersonic Compressible Fluid Flow Using High-Speed Interferometry.

This paper presents a very effective interference technique for the sensing and researching of compressible fluid flow in a wind tunnel facility. The developed technique is very sensitive and accurate, yet easy to use under conditions typical for aerodynamic labs, and will be used for the nonintrusive investigation of flutter in blade cascades. The interferometer employs a high-speed camera, fiber optics, and available "of-the-shelf" optics and optomechanics. The construction of the interferometer together with the fiber optics ensures the high compactness and portability of the system. Moreover, single-shot quantitative data processing based on introducing a spatial carrier frequency and Fourier analysis allows for almost real-time quantitative processing. As a validation case, the interferometric system was successfully applied in the research of supersonic compressible fluid discharge from a narrow channel in a wind tunnel. Density distributions were quantitatively analyzed with the spatial resolution of about 50 µm. The results of the measurement revealed important features of the flow pattern. Moreover, the measurement results were compared with Computational Fluid Dynamics (CFD) simulations with a good agreement.

Parameter optimization of frequency sweeping digital holography for the measurement of ground optical surfaces.

This paper describes the dependence of the precision of digital holographic methods on measurement parameters. The predominantly discussed parameters are illumination intensity and its homogeneity, surface microroughness, the influence of measurement geometry, as well as object shape, since most of them can be optimized by experimental arrangement. Frequency sweeping digital holography as well as dual-wavelength digital holography in the Fourier arrangement are tested and the results are discussed. It transpires that the methods are not very sensitive to object microroughness or overall reflectivity. Instead, it is the similarity of signal and reference waves that has the highest impact on measurement. After parameter optimization, the holographic methods can be advantageously used for ground surface measurements in optical workshops.

Subaperture stitching computation time optimization using a system of linear equations.

Measurement of large or aspheric optical surface shapes as a single aperture using interferometry is problematic for many reasons. A typical problem is the numerical aperture limitation of the interferometer transmission element and the surface slope deviation of aspheres. This deviation typically causes vignetting and spatial aliasing on the camera. A solution is subaperture measurement and subsequent subaperture stitching. A stitching algorithm, in principle, uses overlaps between subapertures to eliminate aberrations of each subaperture to obtain a full aperture for further analysis. This process is computation time demanding and requires optimization in order to obtain a result in a reasonable time to reduce, in turn, the overall manufacturing time. In this paper, a novel, to the best of our knowledge, and fast stitching method based on a system of linear equations is proposed and mathematically described. The developed method was compared with other algorithms, and theoretical computation complexity was calculated and compared. The method was tested practically, with real data measured on spherical surfaces using QED ASI (QED Technologies aspheric stitching interferometer) and an experimental interferometer, and the results are presented. Stitching quality was quantified for results and compared to other algorithms.

Measurement of radius of curvature directly in the interferometer confocal position.

This paper presents a new method for radius of curvature measurement by interferometers. The radius measurement is carried out directly in the interferometer confocal position without the need for a specific hardware and thus allows us to measure a much more diverse range of optical surfaces than standard methods. The method is based on measuring a number of phase maps and displacements at several steps through the confocal null position. Radius of curvature is then computed as the tangent slope of the measured defocus-displacement pair values in the confocal position. A relative accuracy of the method is approximately 0.05%, which makes the method suitable for a vast number of applications. Results of the method are verified using standard confocal cat's eye technique.

Absolute interferometry for fast and precise radius measurement.

A novel radius of the curvature measurement method for optical spherical surfaces using absolute interferometry is proposed. A measurement setup is designed and built around a common-path Fizeau interferometer. The cavity length (volume of air between reference and tested surfaces) can be measured by the absolute wavelength tuning interferometry. An interconnection of data from three different tunable laser diodes (central wavelengths 780, 785 and 852 nm) allows us to measure the cavity length with uncertainty from tens to hundreds of nanometres. Once the reference radius of curvature is known/measured/calibrated, the radius of surface under test can be computed applying the value of the cavity length. The radius of curvature is measured directly in confocal position of the interferometer with relative precision of about 10 ppm. Moreover, unlike standard radius measurement by interferometry, the uncertainty of the introduced method can be optimized by selecting a suitable transmission sphere. In the paper, the method is described, tested, and verified by measuring several specimens featuring different radii of curvature. The results are analysed and furthermore compared to other measurement device.

Multiple angle digital holography for the shape measurement of the unpainted tympanic membrane.

The shape of the tympanic membrane (TM) plays an important role in sound transmission through the ear for hearing. Previously we developed a high-speed holographic system employing a tunable wavelength laser for rapid TM shape measurement. However, the tunable laser illumination was not sufficient to measure the shape of the unpainted TM due to the semi-transparency of the TM and short exposure time of the camera. This paper presents a new multiple angle illumination technique that allows us to use a higher power single wavelength laser to perform shape measurements on the unpainted TM. Accuracy of the new method is demonstrated by a measure of a step gauge provided by the National Institute of Standards and Technology. We successfully applied the new shape measurement method on a fresh postmortem human TM without any paint.

High-Speed Holographic Shape and Full-Field Displacement Measurements of the Tympanic Membrane in Normal and Experimentally Simulated Pathological Ears.

To improve the understanding of the middle-ear hearing mechanism and assist in the diagnosis of middle-ear diseases, we are developing a high-speed digital holographic (HDH) system to measure the shape and acoustically-induced transient displacements of the tympanic membrane (TM). In this paper, we performed measurements on cadaveric human ears with simulated common middle-ear pathologies. The frequency response function (FRF) of the normalized displacement by the stimulus (sound pressure) at each measured pixel point of the entire TM surface was calculated and the complex modal indicator function (CMIF) of the middle-ear system based on FRFs of the entire TM surface motions was used to differentiate different middle-ear pathologies. We also observed changes in the TM shape and the surface motion pattern before and after various middle-ear manipulations. The observations of distinguishable TM shapes and motion patterns in both time and frequency domains between normal and experimentally simulated pathological ears support the development of a quantitative clinical holography-based apparatus for diagnosing middle-ear pathologies.

Surface topography measurement by frequency sweeping digital holography.

High-precision measurements of mechanical parts' surface topography represent an essential task in many industry sectors. Examples of such tasks are, e.g., precise alignments of opto-mechanical systems, large object deformation measurements, evaluation of object shape, and many others. Today, the standard method used for such measurements is based on use of coordinate measuring machines (CMMs). Unfortunately, CMMs have severe shortcomings: low measurement point density, long measurement time, risk of surface damage, etc. Indeed, the measurement time rapidly increases with the object complexity and with the density of measurement points. In this paper, we have developed a method for surface topography measurements called "frequency sweeping digital holography" (FSDH). Our developed FSDH method is based on the principles of wavelength scanning interferometry. It allows surface topography measurements of objects with a diameter of several hundred of mms and a high axial accuracy reaching 10 µm. The greatest advantage of the presented FSDH is the fact that the surface topology data are captured in a motionless manner by means of a relatively simple setup. This makes the FSDH method a suitable technique for topography measurements of objects with complex geometries made of common materials (such as metals, plastics, etc.), as well as for the characterization of complex composite structures such as acoustic metamaterials, active acoustic metasurfaces, etc. Measurement method principles, setup details, lateral resolution, and axial accuracy are discussed.

General temperature field measurement by digital holography.

This paper presents a digital holographic method for measurement of periodic asymmetric temperature fields. The method is based on a modified Twyman-Green setup having double sensitivity. For measurement only one precisely synchronized and triggered digital camera is used. The periodicity and self-similarity of each cycle of the measured phenomenon combined with the precisely synchronized camera capture allow one to obtain data later used for three-dimensional (3D) measurement. The reconstruction of 3D temperature field is based on tomographic approach.

Disc piezoelectric ceramic transformers.

In this contribution, we present our study on disc-shaped and homogeneously poled piezoelectric ceramic transformers working in planar-extensional vibration modes. Transformers are designed with electrodes divided into wedge, axisymmetrical ring-dot, moonie, smile, or yin-yang segments. Transformation ratio, efficiency, and input and output impedances were measured for low-power signals. Transformer efficiency and transformation ratio were measured as a function of frequency and impedance load in the secondary circuit. Optimum impedance for the maximum efficiency has been found. Maximum efficiency and no-load transformation ratio can reach almost 100% and 52 for the fundamental resonance of ring-dot transformers and 98% and 67 for the second resonance of 2-segment wedge transformers. Maximum efficiency was reached at optimum impedance, which is in the range from 500 Ω to 10 kΩ, depending on the electrode pattern and size. Fundamental vibration mode and its overtones were further studied using frequency-modulated digital holographic interferometry and by the finite element method. Complementary information has been obtained by the infrared camera visualization of surface temperature profiles at higher driving power.

Measurement of piezoelectric transformer vibrations by digital holography.

A method for the measurements of the out-of-plane displacement on the surface of vibrating object is presented herein. This method is based on frequency-shifted time-averaged digital holographic interferometry, employing the principle of phase shifting. This approach allows for significant noise reduction, which results in high sensitivity of measurements. This method makes it possible to measure vibrations with amplitudes in the nanometer range over the whole measured surface. This method was applied to the visualization of the out-of-plane vibration modes of piezoelectric transformers. The amplitude and modal shapes were measured with a very high resolution. Furthermore, aspects influencing the measurement errors are discussed and the measurement results by holographic method were compared with the well-established single-point laser interferometry measurement method.