Lloyd's Mirror Interferometer Research Articles

Wide field 3D optical profilometry using a diffraction Lloyd's mirror interferometer.

Interference fringe projection is used as a non-contact optical profilometry method for accurate 3D measurements. In interferometric fringe projection schemes, the maximum measurable size of the test object is limited by the optics of the interferometer. In this work, we report the application of a diffraction Lloyd's mirror interferometer (DLMI) as a wide-field sinusoidal fringe projection system for 3D shape measurement. The DLMI works on diffracted light and therefore generates interference fringes over a large area. This enables measurement of large objects using DLMI as compared to a conventional Lloyd's mirror interferometer. The performance of the proposed system is evaluated in terms of its stability and reproducibility of the results through measurement of the standard deviation in the phase values.

Demonstration of a non-orthogonal Lloyd's mirror interferometer with a spatial light modulator for arbitrary two-dimensional pattern fabrication.

A new, to the best of our knowledge, method of generating interference patterns based on a non-orthogonal Lloyd's mirror interferometer with a spatial phase modulation is proposed. In the proposed method, a spatial light modulator (SLM) is introduced to a conventional non-orthogonal Lloyd's mirror interferometer so that arbitrary interference patterns, such as line interference patterns with varied line-spacing or two-dimensional patterns, can be generated by controlling the wavefronts of the laser beams at each position on the substrate. In this paper, as the first step of the research, the feasibility of the proposed method is theoretically confirmed by calculating interference patterns to be obtained when a spatial modulation of the phase delay is applied to the laser beams. A prototype of a non-orthogonal one-axis Lloyd's mirror interferometer with an SLM in its optical path is also designed and constructed. Some basic experiments are carried out to demonstrate the feasibility of the generation of interference patterns having varied line-spacing and two-dimensional patterns by the proposed method.

Development of dielectric-film-based polarization modulation scheme for patterning highly uniform 2D array structures with periodic tunability

A passively polarized holographic lithography system is proposed for fabricating highly uniform 2D crossed-array structures with periodic tunability and high throughput. The dielectric-film-based polarization modulation scheme is applied to an orthogonal two-axis Lloyd's mirror interferometer to guide the polarization modulation at the interfaces of the mirrors and simplify the exposure-system configuration for large-area fabrication. The proposed polarization-modulation system can fabricate stable large-area (30 mm × 30 mm) array structures with a wide period range from 742 to 1500 nm. Moreover, the established polarization-modulation model could be expanded with multiple dielectric films for attaining higher periodic tunability.

Effect of quality of opto-mechanical components on fringes of diffraction Lloyd mirror interferometer

Diffraction Lloyd mirror interferometer (DLMI) is a relatively new interferometer where interference fringes are generated by superposition of two diffracted beams instead of two geometrical beams of light. The interferometer is suitable for performing basic investigations on diffraction and interference of light. In this work, a number of set-up parameters determining the performance of DLMI including characteristics of knife-edge, quality of mirror, quality of lenses, and effect of algorithm, are experimentally studied and reported for the first time. The effect of these parameters on interference fringes of DLMI is evaluated in terms of change in average intensity, signal to noise ratio (SNR) and contrast of the fringes. By optimizing above parameters, a DLMI set-up is realized and used for characterization of silicon optics fabricated using the single point diamond turning process. The validation results by a commercial optical profiler confirms the effectiveness of DLMI system. This study would provide useful reference for setting up the DLMI system for different applications such as optical profilometry, optical metrology, and to study the diffraction of light etc.

Comparison of sensitivity to beam collimation of the holographic shearing interferometer with the wedge plate shearing interferometer and the Talbot shearing interferometer.

High sensitivity of collimation testing equipment is desirable where collimated beams are used for precise and accurate measurements. Precision in the setting of collimation depends on the sensitivity of the testing equipment. In the present work, sensitivity to beam collimation of the recently reported holographic shearing interferometer (HSI) [J. Opt.20, 055603 (2018)JOOPDB0150-536X10.1088/2040-8986/aab6dc] is measured and compared with sensitivities of other collimation testing techniques based on the wedge plate shearing interferometer and the Talbot shearing interferometer. For a test beam of diameter 25 mm from an He-Ne laser and displacement of the collimating lens by 1 mm from the collimation position, the Talbot shearing interferometer shows a rotation of interference fringes from the horizontal direction by 2°, the wedge plate shearing interferometer shows 20°, and the HSI shows 25°. Sensitivity is also presented in terms of measured slopes of phase maps of the recorded interferograms for a 1 mm displacement of the collimating lens and is obtained as 0.98 mrad, 15 mrad, and 19 mrad corresponding to the Talbot shearing interferometer, the wedge plate shearing interferometer, and HSI, respectively. The effect of decollimation of the laser beam on the interference fringes of diffraction of the Lloyd mirror interferometer is also demonstrated. Theoretical concepts and experimental results are presented and discussed for the above-mentioned beam collimation testing techniques.

Design optimization of a non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings

An optimized beam expansion assembly is newly designed for a non-orthogonal two-axis Lloyd's mirror interferometer to fabricate large-area two-dimensional (2D) diffraction scale gratings in a small-scale manufacturing facility or a research laboratory. Theoretical calculations are at first carried out to quantitatively estimate the influences of the coherence length and the Gaussian light intensity distribution of a collimated laser beam, which is projected onto a mirror-substrate assembly for the generation of interference fringe fields on a substrate. Design optimization of the interferometer is then carried out in such a way that a beam shaper, which contributes to obtain a flat-top light intensity distribution in the collimated laser beam and is expected to reduce the amplitude deviation of the developed pattern structures as well as the pattern exposure time, is integrated into the beam expansion assembly. The feasibility of the newly developed beam expansion assembly is demonstrated through fabricating a 100 mm × 100 mm 2D scale grating having pattern structures with uniform amplitude of approximately 500 nm and a short period of 1 μm.

Fabrication of micrometer-scale surface relief gratings in azobenzene molecular glass films using a modified Lloyd's mirror interferometer

Large-scale surface relief diffraction gratings with pitches up to 20 μm were fabricated in thin films of azobenzene molecular glass using a single-step and mask-less photolithography process. A modified Lloyd's mirror interferometer having two degrees of freedom generated an interference pattern that was incident on the azobenzene films. Some of the fabricated gratings had non-periodic profiles resulting from the superposition of multiple sine waves, while others had periodic blazed sawtooth and Dirac comb profiles. Furthermore, careful selection of the experimental parameters resulted in gratings with a beat interference profile having a clearly-visible modulation envelope. A theoretical framework was developed to successfully explain the obtained grating profiles.

A compact two-axis Lloyd's mirror interferometer for scale grating fabrication

A compact two-axis Lloyd's mirror interferometer for scale grating fabrication

Optical spectrometer based on continuously-chirped guided mode resonance filter.

In this work we introduce a tunable GMR filter based on continuously period-chirped (ΔP = 130 nm) gratings using a Ta2O5 waveguide layer with graded thickness (ΔT = 36 nm). The structure of the gradient-period grating is defined using a modified Lloyd's mirror interferometer with a convex mirror, and Ta2O5 film used for the gradient is deposited using masked e-beam evaporation. The as-realized chirped GMR filter provides sharp transmission dips at resonant wavelengths with a filter bandwidth of approximately 4.2 nm and 0.78 nm when respectively applied to TE and TM polarized light under normal incidence. Gradually sweeping the chirped GMR filter makes it possible to monotonically sweep through resonant wavelengths from 500 to 700 nm, while maintaining stable filter bandwidth and transmission intensity. The optical spectrum of the incoming light can then be loyally reconstructed accordingly. We successfully demonstrate the spectrum reconstruction of a white light emitting diode and a dual-peak laser beam using the proposed chirped GMR filter as a dispersive device.

Inscription and analysis of non-uniform diffraction gratings in azobenzene molecular glass thin films.

Non-uniform surface relief diffraction gratings were laser-inscribed on azobenzene molecular glass thin films using a modified Lloyd's mirror interferometer. The azobenzene films were exposed to an adjustable interference pattern produced by the recombination of collimated and spherically divergent laser wave fronts. The localized pitch, grating vector orientation and depth of the resulting non-uniform gratings were measured using an atomic force microscope and a theoretical model was analytically developed to explain the experimental results. The fabricated gratings exhibited a chirping or pitch variation along the imposed X-axis as well as an angular change in the grating vector orientation along the imposed Y-axis. Studies were conducted on various non-uniform grating configurations having central pitches of 500 nm, 1000 nm, 1500 nm and 2000 nm.

Hot and dense plasma probing by soft X-ray lasers

Soft X-ray lasers, due to their short wavelength, its brightness, and good spatial coherence, are excellent sources for the diagnostics of dense plasmas (up to 1025 cm−3) which are relevant to e.g. inertial fusion. Several techniques and experimental results, which are obtained at the quasi-steady state scheme being collisionally pumped 21.2 nm neon-like zinc laser installed at PALS Research Center, are presented here; among them the plasma density measurement by a double Lloyd mirror interferometer, deflectometer based on Talbot effect measuring plasma density gradients itself, with a following ray tracing postprocessing. Moreover, the high spatial resolution (nm scale) plasma images can be obtained when soft X-ray lasers are used.

Design and testing of a compact non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings

A compact and stable two-axis Lloyd’s mirror interferometer based on a new non-orthogonal type of mirror-substrate assembly is designed for fabrication of 100 mm × 100 mm large-area two-dimensional (2D) diffraction scale gratings in a research laboratory or a small-scale manufacturing facility. At first, the required mirror sizes used in the new non-orthogonal type and the conventional orthogonal type are compared based on geometrical analysis. It is identified that the width of the mirror can be reduced to half in the non-orthogonal type while the required mirror height and the expanded laser beam diameter are comparable to those in the orthogonal type. The shorter mirror width makes it possible to design a compact mirror-substrate assembly so that the overall interferometer can be realized in an overall size of 1480 mm × 730 mm for mounting on a commercially available general-purpose 1500 mm × 1000 mm vibration isolation table for use in research laboratories. It is then verified by simulation that the selected laser source and the designed beam expansion assembly, which are the other main parts of the interferometer, are effective for fabricating the designed grating structures. Experiments are also carried out to demonstrate the feasibility of the constructed interferometer for fabricating 100 mm × 100 mm 2D scale gratings with a short period of 1 μm.

Optimal polarization modulation for orthogonal two-axis Lloyd's mirror interference lithography.

Polarization control is of vital importance in two-axis Lloyd's mirror interference lithography to achieve the preferred interference fringes. In this work, we first establish a three-dimensional polarization ray-tracing model to trace the evolution of polarization states of incident beams through the corner-cube-like interferometer unit of an orthogonal two-axis Lloyd's mirror interferometer. With the established model, we then derive the optimal combination of initial polarization directions of the incident beams according to the orthogonality of polarization states and the contrast of interference fringes. The comparison between the simulated and experimental interference fringes obtained under different combinations of initial polarization states of incident beams verify the feasibility of the established model and the achieved optimal polarization modulation.

Fabrication of a two-dimensional diffraction grating by a two-axis Lloyd's mirror interferometer

Fabrication of a two-dimensional diffraction grating by a two-axis Lloyd's mirror interferometer

Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer.

This paper presents a detailed analysis on the influence of misalignment errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer, which can fabricate two-dimensional grating structures in a single exposure. In an ideal condition, defect-free two-dimensional grating structures can be fabricated by the interferometer. However, in a real case, visible stripes caused by misalignment errors of the optical components in the interferometer always appear on the fabricated grating structures. In this paper, theoretical analysis and experiments are carried out to analyze the influences of the misalignment errors of the optical components in the orthogonal two-axis Lloyd's mirror interferometer.

Optical mosaic method for orthogonally crossed gratings by utilizing information about both main periodic directions simultaneously

We present a method to make optical mosaic orthogonally crossed gratings by utilizing information about both main periodic directions simultaneously. The whole mosaic system for orthogonally crossed gratings is set up based on the dual Lloyd's mirror interferometer that fabricates orthogonally crossed gratings through a single exposure. The interference fringes formed by the diffractions of the exposure beams from the exposed grating areas are used as the reference to fine tune the position and attitude of the exposure beams relative to the substrates during consecutive exposures. A procedure to make mosaic for two main periodic directions simultaneously is proposed based on the presupposition that the angle between two sets of main lattice lines is constant during the mosaic. Experimentally we made a 2×1 mosaic crossed grating with a period of 574nm in (30+30) mm ×35mm area. The peak-valley errors of the (−1, 0)th- and (0, −1)st-order diffraction wavefronts over the whole mosaic grating area are 0.104λ and 0.163λ, respectively.

Period-chirped gratings fabricated by laser interference lithography with a concave Lloyd's mirror.

We developed a laser interference lithography (LIL) system for fabrication of period-chirped gratings, which would be useful for sophisticated optical components. Despite its simplicity, the developed LIL system, based on a Lloyd's mirror interferometer with a cylindrically concave mirror, can generate chirped gratings, yet over a large area at high throughput owing to the nature of LIL. We have derived exact theoretical equations needed for system design, built the LIL system, and subsequently realized period-chirped gratings. A fabricated sample whose center period is Λ≈600 nm exhibits a continuous period variation of ΔΛ=92 nm across 17mm width.

Investigation on the three-dimensional light intensity distribution of the fringe patterns generated by a modified two-axis Lloyd's mirror interferometer

Investigation on the three-dimensional light intensity distribution of the fringe patterns generated by a modified two-axis Lloyd's mirror interferometer

A simplified method for generating periodic nanostructures by interference lithography without the use of an anti-reflection coating

Interference lithography has proven to be a useful technique for generating periodic sub-diffraction limited nanostructures. Interference lithography can be implemented by exposing a photoresist polymer to laser light using a two-beam arrangement or more simply a one beam configuration based on a Lloyd's Mirror Interferometer. For typical photoresist layers, an anti-reflection coating must be deposited on the substrate to prevent adverse reflections from cancelling the holographic pattern of the interfering beams. For silicon substrates, such coatings are typically multilayered and complex in composition. By thinning the photoresist layer to a thickness well below the quarter wavelength of the exposing beam, we demonstrate that interference gratings can be generated without an anti-reflection coating on the substrate. We used ammonium dichromate doped polyvinyl alcohol as the positive photoresist because it provides excellent pinhole free layers down to thicknesses of 40 nm, and can be cross-linked by a low-cost single mode 457 nm laser, and can be etched in water. Gratings with a period of 320 nm and depth of 4 nm were realized, as well as a variety of morphologies depending on the photoresist thickness. This simplified interference lithography technique promises to be useful for generating periodic nanostructures with high fidelity and minimal substrate treatments.

Method to fabricate orthogonal crossed gratings based on a dual Lloyd's mirror interferometer

We propose a dual Lloyd's mirror interferometer with two mutually perpendicular mirrors to fabricate orthogonal crossed gratings through a single exposure. Theoretical analysis shows that in this interferometer the angle between two main periodic directions of the crossed grating is solely determined by the normal directions of the two Lloyd's mirrors and the substrate. To verify this theoretical prediction, four groups of crossed gratings were fabricated. The measurement results agree well with the theoretical relationship.