Differential Heterodyne Research Articles

Implementation of the coupled-wave method for V-shaped groove characterization with a scanning differential heterodyne microscope

The image formation theory is presented for scanning differential heterodyne microscope respect to triangular-shaped grooves used for plasmon-polariton waveguiding. The scattering problem of the illuminating probe beams focused on the object surface is resolved with rigorous coupled-wave analysis (RCWA) for groove corrugated grating etched in a substrate with the finite conductivity. To adapt the RCWA method for SDHM the problems were considered associated with a discretization of the diffracted field and sampling the focused probe beams. The focused beams are expanded in terms of plane waves so that the each chosen incident wave is order of one another and then the diffraction problem is solved for every plane wave of TE polarization. The groove was decomposed into thin layers in which the permittivity and electromagnetic field are expanded in Fourier series. The diffraction of the probe beams by triangular groove was analyzed, at that the convergence of modulus and phase responses of SDHM in dependence of the number of the layers and the number of Fourier modes in optical field expansion was investigated. The elaborated algorithm was used for the simulation of differential responses from triangular grooves with various parameters.

Determining the complex point-spread function of a scanning differential heterodyne microscope

For a scanning differential heterodyne microscope, the two-dimensional point spread function and the pupil function are determined from experimental measurements of the intensity distribution of a probing beam. The phase components of these functions were restored from the measured distributions using the Gerchberg-Saxton algorithm. Based on the two-dimensional pupil function, the three-dimensional point-spread function is determined in the scalar approximation using the Debye integral. The aberration function of the microscope is analyzed from the viewpoint of the composition of aberrations and method of their balancing. The focusing adjustment criterion of the microscope for an object under study by the phase response from the test structure is considered.

Nano-optofluidic detection of single viruses and nanoparticles.

The reliable detection, sizing, and sorting of viruses and nanoparticles is important for biosensing, environmental monitoring, and quality control. Here we introduce an optical detection scheme for the real-time and label-free detection and recognition of single viruses and larger proteins. The method makes use of nanofluidic channels in combination with optical interferometry. Elastically scattered light from single viruses traversing a stationary laser focus is detected with a differential heterodyne interferometer and the resulting signal allows single viruses to be characterized individually. Heterodyne detection eliminates phase variations due to different particle trajectories, thus improving the recognition accuracy as compared to standard optical interferometry. We demonstrate the practicality of our approach by resolving nanoparticles of various sizes, and detecting and recognizing different species of human viruses from a mixture. The detection system can be readily integrated into larger nanofluidic architectures for practical applications.

Differential heterodyne detection with diffractive optics for multidimensional transient-grating spectroscopy

Heterodyne detection with a local oscillator generated by a diffractive optic provides good phase stability, but suffers from interfering single-beam-bleach signals. This interference is a problem in four-beam transient gratings, but becomes more severe in higher order transient gratings. A simple and low noise method to eliminate this interference is demonstrated in both a four-wave-mixing, first-order-transient-grating experiment and in a six-wave-mixing, second-order-transient-grating experiment.

Interferometry based high-precision dilatometry for dimensional characterization of highly stable materials

We present an optical dilatometer for high-accuracy and high-resolution absolute measurement of the linear coefficient of thermal expansion (CTEl). Based on a highly symmetric differential heterodyne interferometer, dimensional changes of a tubular shaped specimen under controlled thermal conditions can be characterized. Our measurement facility is located in vacuum where the test specimen can be temperature controlled in a temperature range between 20 °C and 60 °C. A thermally stable support and two identical isostatic mirror clamps were specifically designed to fix a reference and a measurement mirror inside the tube enabling a measurement, where no load in the axial direction was applied to the device under test (DUT). We measured the linear CTE of two carbon-fibre reinforced plastic (CFRP) tubes with different predicted linear CTEs at room temperature: −0.647 × 10−6 K−1 and 0 ± 2.5 × 10−9 K−1, respectively. Currently, we are investigating the manufacture limitations of the CFRP and the limitations of our apparatus in terms of measurement accuracy. In the next step, we will characterize a specifically manufactured zero-class Zerodur™ tube with a CTEl value <10 × 10−9 K−1. Due to its high thermal stability and non-directional structural isotropy this material has been chosen for macroscopic calibration of the metrology system. The results of these measurements will thus provide the resolution limitations of our facility and can be taken as an absolute accuracy reference.

A polarization method for characterizing rectangular microgrooves from the phase response of a differential heterodyne microscope

The phase and modulus responses from rectangular microgrooves are modeled for two basic polarizations of probe radiation based on a response formation algorithm in a scanning differential heterodyne microscope and taking into account the rigorous theory of diffraction. The dependences of the phase contrast on the depth and the width of the microobject are calculated based on the responses obtained. The possibilities for simultaneous characterizing microgrooves with respect to their depth and width are analyzed. The parameters in ranges of phase dislocations and weak signals are proposed to be determined from the dependences of the phase and amplitude contrasts on the groove depth calculated for responses detected out of the center of the Fourier plane of the microscope.

A double common-path heterodyne interferometer for the measurement of flying height modulation

A double common-path differential heterodyne interferometer is proposed to measure the flying height modulation (FHM) of a slider in a hard disk drive. A transverse Zeeman He–Ne laser is employed as the light source and high-speed phase measurement is applied for signal processing. The resolution and the sampling frequency of FH measurement are 0.1 nm and 500 kHz, respectively. According to the symmetrical optical path design, the environmental noise and Abbe error from the disk can be adaptively compensated. The experimental results show that the stability of the system is sub-nanometer in a normal laboratory without air conditioning, and the FHM of ±3 nm is achieved when the pitch of the rotating disk is around 1.2 µm.

Differential heterodyne interferometer for measuring thickness of glass panels

Differential heterodyne interferometer is applied for measuring spatial thickness variations across glass panels of liquid-crystal displays. This system uses the Zeeman laser as a source of two-frequency shifted orthogonally linearly polarized probe waves, passing through the glass in two spatially separated points. These waves are then recombined in a single beam to produce the intermediate frequency signal with the phase proportional to the thickness gradient of a glass sample. The phase of the intermediate signal is measured against the laser reference by means of a lock-in amplifier, and finally real-time integration provides the thickness variation. Since spatial separation of the probe beams is only 1.35 mm good approximation for the thickness gradient is achieved. Detailed design of the interferometer and experimental results on real samples are presented.

Beam Scanning Confocal Differential Heterodyne Interferometry

This article presents a new approach to the design of confocal differential heterodyne interferometer (CDHI), which is a combination of differential heterodyne interferometer (DHI) with confocal laser scanning microscopy (CLSM). The CDHI can measure a step height over a quarter of wavelength of the light source, which can not be accurately measured by DHI and CLSM, respectively. The approach is that it utilizes a beam-scanning method instead of transporting a sample to be measured. The measurement results carried out for samples having step height are found to be comparable in precision with those measured by commercial scanning electron microscopes.

High Precision Measurement of 3D Profile Using Confocal Differential Heterodyne Interferometer

The differential heterodyne interferometer (DHI) is suitable for precise measurement of step height and line width, since its differential configuration can significantly reduce disturbances from the environment [1,2]. Like most phase measuring interferometers, however, the DHI is limited, in that it can obtain only the phase from 0 to 2π, because of the sinusoidal nature of the optical interference involved. Thus, the measurable step height is limited to one quarter of the wavelength of the light source. This study describes a confocal differential heterodyne interferometer (CDHI) for measuring step heights of several micrometers, with a high resolution and line width with high repeatability. The CDHI has a simple structure and rapid measurement speed.

Optoelectronic implementation of a 256-channel sonar adaptive-array processor

We present an optoelectronic implementation of an adaptive-array processor that is capable of performing beam forming and jammer nulling in signals of wide fractional bandwidth that are detected by an array of arbitrary topology. The optical system makes use of a two-dimensional scrolling spatial light modulator to represent an array of input signals in 256 tapped delay lines, two acousto-optic modulators for modulating the feedback error signal, and a photorefractive crystal for representing the adaptive weights as holographic gratings. Gradient-descent learning is used to dynamically adapt the holographic weights to optimally form multiple beams and to null out multiple interference sources, either in the near field or in the far field. Space-integration followed by differential heterodyne detection is used for generating the system's output. The processor is analyzed to show the effects of exponential weight decay on the optimum solution and on the convergence conditions. Several experimental results are presented that validate the system's capacity for broadband beam forming and jammer nulling for linear and circular arrays.

Investigation of diffraction gratings with the use of a differential heterodyne microscope

A theory of image formation in a scanning differential heterodyne microscope is developed using the results of observations of a metallized periodic structure with a rectangular profile. The phase and amplitude response functions are calculated for TE and TM polarizations. It is demonstrated that the width of grating elements can be measured with a superresolution. The experimental phase and amplitude responses from a metallized grating with a trapezoidal profile are obtained and compared with the results of theoretical calculations.

Object characterization with a differential heterodyne microscope

One-dimensional image formation theory is presented for a scanning differential heterodyne microscope based on a balanced scheme for the Mach–Zehnder interferometer with a Bragg cell as the beam splitter. The interferometer allows coherent detection of a complex signal in the Fourier plane. The scattering problem of illuminating beams focused on the object was solved with rigorous diffraction theory for a perfectly conducting groove-corrugated grating using the modal method. The responses from step-like micro-objects have been calculated for both TE and TM (transverse electric and magnetic) polarizations for a range of heights. The experimental amplitude and phase responses from thick dielectric steps on silicon substrates (with and without evaporation of a thin gold film) are presented for various intervals between illuminating spots.

Differential wavelength-scanning heterodyne interferometer for measuring large step height.

An interferometer based on the differential heterodyne configuration and wavelength-scanning interferometry for measuring large step heights is presented. The proposed interferometer is less sensitive to environmental disturbances than other interferometers and can accurately measure interference phases. A tunable diode laser is utilized to illuminate the interferometer and thus solve the phase ambiguity problem. Counting the interference fringes as the wavelength is scanned through a known change in wavelength directly determines the step height. Three gauge blocks of different lengths, 5, 10, and 50 mm, are individually wrung on a steel plate to simulate large step heights. Comparing the results measured by the proposed interferometer with those by the gauge block interferometer reveals that the accuracy is approximately 100 nm.

Characteristics of the differential heterodyne microscope, studied by means of a periodic test structure

Characteristics of the differential heterodyne microscope, studied by means of a periodic test structure

Heterodyne Detection of Synchrotron Radiation

A time integral method for the study of resonant nuclear scattering of synchrotron radiation in the forward direction is presented. The method relies on the interference of radiation scattered by nuclei in two samples, one moving with respect to the other. The method, termed heterodyne detection of synchrotron radiation, gives the same information on hyperfine parameters as the well known differential method. The general formalism is developed for the case where the reference is a single line sample and the investigated sample has magnetic or quadrupole splitting. The first experiments are discussed. A comparison of time differential synchrotron radiation spectroscopy, heterodyne detection and Mossbauer spectroscopy is given.

Investigation on phase jump in a differential interferometer

This article presents a new phase jump phenomenon in a differential heterodyne interferometer. When the intensity of one arm of an interferometer changes from greater to less (or less to greater) than that of another, a phase jump of 180° will take place if the phase difference between two arms is prefixed at π. We call this phenomenon phase jump. To demonstrate phase jump, a modified differential heterodyne interferometer has been setup. The intensity of one arm is modulated as the arm is scanning across an edge. Both theoretical and experimental investigations are conducted in detail. The theoretical and experimental results indicate that the phase slope of the phase jump is infinite and the amplitude of output signal is zero when a phase jump occurs. Meanwhile the position of phase jump is very sensitive to the displacement. Therefore, both phase and amplitude signals of phase jump are suitable for precise position index and may find wide potential applications in the fields of edge detection, alignment, optical storage, and so on.

Method for edge detection based on phase jump in a differential interferometer

We describe a new method for edge detection that uses polarization mixing in a differential heterodyne interferometer. When one of the focused beams of the interferometer scans across an edge, a phase jump of 180 degrees takes place in the very small region of the edge if certain conditions are satisfied. We call this phenomenon phase jump. The conditions in which phase jump can occur are given. The theoretical analysis shows that the slope of a phase jump is infinite and is not affected by step height, the vibration of the sample, or the intensity variation of the light source. Therefore phase jump can be used as the precise index for edge detection. The experimental results show good agreement with the theoretical analysis.

Highly Sensitive and Widely Dynamic Fiber-Coiled Deformation Sensor Immune from External Disturbances

This paper describes a double fiber-coiled interferometric deformation sensor fabricated using paired polarization maintaining single-mode fibers. A change in bending-induced birefringence plays a fundamental role in the sensor performance as the fiber-coil is being deformed across its cross-section. Differential optical heterodyne detection processes allow us to implement two-mode operations; one is widely dynamic operation and the other highly sensitive operation around a target region. The deformation sensitivity for one-turn fiber-coil is 2.5 deg/mm for the widely dynamic operation, whereas 9.5X10 deg/mm for the highly sensitive operation. The double fiber-coiled deformation sensor can eliminate external, undesirable temperature disturbances.

Biological imaging using fast laser scanning heterodyne differential phase confocal microscopes

Differential phase microscopy has proved invaluable in the study of live, unstained, thin biological samples because of its ability to image changes in refractive index and topography. Similarly, because of its optical sectioning capability, confocal microscopy is now a well‐established technique in the study of relatively thick live biological samples. This paper describes the development and application of two differential phase heterodyne confocal microscopes, and compares their performance. The use of these systems for imaging in‐vitro cell and tissue cultures is considered and compared with confocal reflection microscopy. It is demonstrated that the differential phase capability reveals subcellular structural information not readily seen in the confocal reflection images. This technique opens up the possibility of imaging thick unstained live tissues, avoiding cell damage and artefacts associated with staining procedures. Furthermore, the differential phase images can be used to provide a visual frame within which stained features can be located.