Differential Heterodyne Microscope Research Articles

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.

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.

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.

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.

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.

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