Heterodyne Microscope Research Articles

Characterization of gap-plasmon-based metasurfaces with scanning white-light interferometry

Subject of study. The possibility of using the well-established method of scanning white-light interferometry (SWLI), implemented as a commercially available device, is studied for characterizing promising metasurfaces based on third-order plasmon resonance. The characteristics of the samples were determined for two types of experimental metasurfaces, namely, for a binary grating with a period of 12.6 µm and a phase gradient grating with a period of 6.75 µm. Objective. The main goals of this study were to test the fundamental possibility of using a commercially available white-light interferometer to determine the phase characteristics of plasmonic metasurfaces and to estimate experimentally the lateral optical resolution in the phase image of metasurfaces. Main results. Although the method of SWLI was originally intended for measuring a geometric microrelief, it was found that it can be used to determine the phase increment of the optical radiation reflected from the studied metasurfaces in the range of 10°–100° with a relative accuracy of approximately 50% without any modification of the signal processing algorithm. The possibility of obtaining a phase mapping of the surface with such accuracy in this configuration is not obvious because the metasurface is a matrix of nanoelements with the same height of 50 nm, and the phase shift in the reflected optical radiation is created due to third-order gap plasmon resonance. On the obtained optical phase images of metasurfaces, unit (single) cells of the metasurface are reliably resolved owing to a sufficiently high lateral resolution (approximately 450 nm). The results of the characterization of metasurfaces obtained using SWLI are compared with those obtained in a laboratory setup using scanning differential heterodyne microscopy (SDHM). Although the SWLI method demonstrates better lateral resolution compared with the SDHM method, it is less accurate in restoring the phase characteristics of metasurfaces with a phase gradient. Practical significance. The results obtained allow us to conclude that the evaluation of the phase optical characteristics of nanostructured plasmonic metasurfaces by the method of SWLI is possible and requires further experimental and theoretical studies.

Characterization of gap-plasmon based metasurfaces using scanning differential heterodyne microscopy

Optical phase-gradient metasurfaces, whose unique capabilities are based on the possibility to arbitrarily control the phase of reflected/transmitted light at the subwavelength scale, are seldom characterized with direct measurements of phase gradients. Using numerical simulations and experimental measurements, we exploit the technique of scanning differential heterodyne microscopy (SDHM) for direct phase and amplitude characterization of gap-plasmon based optical metasurfaces. Two metasurface configurations utilizing the third-order gap surface plasmon (GSP) resonance, representing a binary grating and linear phase gradient, are experimentally characterized with the SDHM operating at the light wavelength of 633 nm. Comparing the experimental performances of these GSP metasurfaces with those expected from the phase and amplitude profiles reconstructed from the SDHM measurements, we verify the efficiency and accuracy of the developed SDHM characterization approach for direct inspection of GSP reflective metasurfaces.

Superresolution effect on a microstep phase image in a laser heterodyne microscope

The possibility of achieving superresolution on a microstep phase image in a laser scanning differential heterodyne microscope is studied both heoretically and experimentally. The superresolution is estimated as the width ratio for the amplitude and phase components of the microscope response measured at half the height of the corresponding parts of the response. It is shown theoretically that superresolution greatly exceeding unity can be achieved for an object in the form of a phase microstep introducing a phase shift equal to π. Superresolution of ∼2 is experimentally obtained for certified test micro-objects. A possibility of tuning a test sample into the superresolution regime by shifting a point photodetector in the microscope’s Fourier plane is demonstrated.

Scanning differential microscopy for characterization of reflecting phase-gradient metasurfaces

Gap-plasmon based phase-gradient metasurfaces operating in reflection are widely used for the realization of diverse flat optical components, ranging from spectropolarimeters to efficient couplers for surface waves. Successful implementation of carefully designed metasurfaces is however often hampered by technological imperfections that could be related to deviations of geometrical parameters of fabricated nanostructures from the designed ones or material properties, such as the metal and/or dielectric susceptibilities, from the handbook data. While the overall performance of fabricated components might indicate the existence of a potential problem, it is very difficult to identify its origin, which, for example, can simply be related to the deviation in only one cell of the metasurface supercell. We suggest exploiting well-developed experimental techniques of scanning differential heterodyne microscopy (SDHM) to characterize fabricated phase-gradient metasurfaces designed to operate in reflection. We further establish that, by carefully measuring the SDHM response of a gradient metasurface, one should be able of detecting small (∼5%) amplitude and phase deviations (with respect to the design values) in the optical field reflected by an individual subwavelength-sized cell of the metasurface supercell.

Optimized method for solving the inverse problem for a triangular plasmonic waveguide using a response of scanning heterodyne microscope

A method proposed previously to solve the inverse problem for triangular plasmonic waveguides using a TE-polarized response of scanning differential heterodyne microscope has been optimized. The use of the phase contrast of microscope response at two wavelengths as initial data made it possible to reduce significantly the solution error and eliminate the instability domains of initial data, in which the solution error dramatically increased. It is demonstrated that the accuracy of determining the waveguide parameters significantly improves in comparison with the case where the amplitude and phase contrast of response at one wavelength are used as initial data. It is shown that the solution of the inverse problem can be further optimized using contrasts of amplitude responses as additional initial data. The dependences of the error of inverse problem solution on the error in determining the initial data are calculated.

Analysis of the accuracy of the inverse problem solution for a differential heterodyne microscope as applied to rectangular plasmonic waveguides

The existence, uniqueness, and stability of the inverse problem solution for a scanning differential heterodyne microscope as applied to rectangular plasmonic waveguides have been analyzed. The consideration is based on an algorithm using a trial-and-error method that we proposed previously to characterize plasmonic waveguides with a triangular profile. The error of the inverse problem (IP) solution is calculated as dependent on the initial data and with allowance for their errors. Instability domains are found for the IP solution, where the solution error sharply increases. It is shown that the instability domains can be eliminated and the accuracy of the IP solution can be significantly improved in the entire range of initial data by taking initial data in the form of two phase responses of the microscope at different wavelengths.

Photothermal raster image correlation spectroscopy of gold nanoparticles in solution and on live cells.

Raster image correlation spectroscopy (RICS) measures the diffusion of fluorescently labelled molecules from stacks of confocal microscopy images by analysing correlations within the image. RICS enables the observation of a greater and, thus, more representative area of a biological system as compared to other single molecule approaches. Photothermal microscopy of gold nanoparticles allows long-term imaging of the same labelled molecules without photobleaching. Here, we implement RICS analysis on a photothermal microscope. The imaging of single gold nanoparticles at pixel dwell times short enough for RICS (60 μs) with a piezo-driven photothermal heterodyne microscope is demonstrated (photothermal raster image correlation spectroscopy, PhRICS). As a proof of principle, PhRICS is used to measure the diffusion coefficient of gold nanoparticles in glycerol : water solutions. The diffusion coefficients of the nanoparticles measured by PhRICS are consistent with their size, determined by transmission electron microscopy. PhRICS was then used to probe the diffusion speed of gold nanoparticle-labelled fibroblast growth factor 2 (FGF2) bound to heparan sulfate in the pericellular matrix of live fibroblast cells. The data are consistent with previous single nanoparticle tracking studies of the diffusion of FGF2 on these cells. Importantly, the data reveal faster FGF2 movement, previously inaccessible by photothermal tracking, and suggest that inhomogeneity in the distribution of bound FGF2 is dynamic.

Characterization of V-shaped plasmon polariton waveguides using a differential heterodyne microscope at single polarization

The possibility of using a scanning differential heterodyne microscope for characterization of V-shaped plasmon waveguides is demonstrated. To characterize a waveguide profile, a specific algorithm based on solution of the inverse problem is proposed. The microscope response library at various waveguide parameters is calculated using the image formation theory and rigorous couple wave analysis for matching with experimentally measured responses. The investigation of stability of the inverse problem solution has revealed unstable zones within specified ranges of waveguide parameters. Further analysis shows that these zones can be shifted with variation of the probing beam wavelength.

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.

Dual‐channel heterodyne microscope: new functions

Quantitative assessment of critical dimensions of sub-wavelength structures, dark-field and bright-field modes of operation, recognition of nonpatterned anisotropic surfaces, and three-dimensional profiling of opaque and transparent samples are the new features of a super-resolution dual-channel heterodyne microscope that was introduced in a previous publication in this journal. The aforementioned modes of operation can be activated by simple rotation of a polarizer or insertion of a polarization-separating prism. Various experimental results are presented, demonstrating new performance capabilities of the heterodyne microscope.

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.

Heterodyne polarimetry technology for inspection of critical dimensions

Heterodyne polarimetry is based on the analysis of phases and polarization states of two frequency shifted cross-polarized waves, generated by Zeeman lasers and their analogs [1]. In semiconductor industry, manufacturing of memory chips depends on the width and aspect ratio of a great number of identical parallel vertical and horizontal word and bit address lines. Such a structure may be considered as a wire grid polarizer for visible optics, and it is reasonable to expect that polarimetry techniques may be efficient for detecting tiny variations in this type of structures on masks and wafers. Currently, both imaging and non-imaging modalities are considered as complementary inspection technologies. The talk will focus on instrumentation, theory, and experimental results of two different inspection tools: scanning polarimeters for mapping variations of critical dimensions over lithography masks and semiconductor wafers, and polarization-controlled dual-channel heterodyne microscope with super-resolution capabilities.

Overall characterization of assembled optical storage devices with a heterodyne microscope: a qualitative comparison with a confocal microscope

We present local profile measurements of inner mirrorlike and external front-end polycarbonate surfaces at the same spot of assembled optical storage devices, a CD and a DVD, performed with a heterodyne scanning interferometer that uses Gaussian beams. We show that the heterodyne interferometer can reproduce the profiles of both surfaces with accurate precision. We describe a procedure for calibrating the instrument based on the measurement of reflecting calibrated gratings. To show the advantages that the heterodyne interferometer represents as a valuable tool for the characterization of optical disks, we include a comparison of experimental results obtained with a confocal microscope under similar working conditions.

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.

Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes

In this paper we derive the three-dimensional scalar theory of the overall imaging process in a high-aperture interference, holographic, and correlation (heterodyne) microscope. The influence of low spatial and temporal coherence of light is completely described by means of a coherent transfer function. The results are compared with those for an ideal confocal microscope.

Improvement of confocal microscope performance by shaped annular beam and heterodyne confocal techniques

In order to further improve the performance of a confocal microscope (CM) used for measurement of surface profiles and 3D microstructures, a shaped annular beam heterodyne confocal measurement method based on annular pupil filter technique and reflection confocal microscopy, is proposed to expand the measurement range and to improve the defocused property of CM. The approach proposed uses a confocal dual-receiving light path arrangement and a heterodyne subtraction of two signals received from detectors with axial offset to enable CM to be used for bipolar absolute measurement and to improve the defocused property of CM, and it uses the annular pupil filter technique to produce a binary optical shaped annular beam, which expands the measurement range by expanding the full-width at half-maximum of intensity curve received from two detectors in a heterodyne confocal microscopy system. Theoretical analyses and experimental results indicate that a shaped annular beam heterodyne microscope has a measurement range expanded from 4 to 14 μm, achieved an axial resolution of 2 nm and improved the defocused property, when ε = 0.5 and NA = 0.65 . It can be therefore concluded that the shaped annular beam heterodyne confocal measuring method proposed is a new approach to ultraprecision measurement of surface profiles and 3D microstructures.

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.

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

Analysis of heterodyne and confocal microscopy for illumination with broad-bandwidth light

Abstract An imaging equation is derived which describes heterodyne microscopy with broad-band light illumination. The impact of spherical aberration resulting from imaging into thick samples is investigated. As in confocal microscopy, the lateral resolution is found to be only weakly affected by moderate spherical aberration. The loss in depth resolution can be strongly reduced by using broad-band light with a short coherence length.