New developments in interferometry

Structured illumination contrast transfer function for high resolution quantitative phase imaging

We report a sub-diffraction resolution imaging of non-fluorescent samples through quantitative phase imaging. This is achieved through a novel application of structured illumination microscopy (SIM), a super-resolution imaging technique established primarily for fluorescence microscopy. Utilizing our contrast transfer function formalism with SIM, we extract the high spatial frequency components of the phase profile from the defocused intensity images, enabling the reconstruction of a quantitative phase image with a frequency spectrum that surpasses the diffraction limit imposed by the imaging system. Our approach offers several advantages including a deterministic, phase-unwrapping-free algorithm and an easily implementable, non-interferometric setup. We validate the proposed technique for high-resolution phase imaging through both simulation and experimental results, demonstrating a two-fold enhancement in resolution. A lateral resolution of 0.814 µm is achieved for the phase imaging of human cheek cells using a 0.42 NA objective lens and an illumination wavelength of 660 nm, highlighting the efficacy of our approach for high-resolution quantitative phase imaging.

Directional phase-unwrapping algorithm and phase shift technique on hydrogel

Refractive index microstructures, which can be written by multiphoton absorption with femtosecond lasers, have many applications. Here we present a directional phase-unwrapping algorithm with phase-shifting technique and apply it to the metrology of hydrogel microstructures. A staircase phase-unwrapping algorithm is demonstrated. This fast quality-guided path phase-unwrapping applies well to situations that are geometrically well defined and is quite tolerant of phase noise. To achieve precise very small phase shifts, we also present a slant angle technique on a DC servo stage along with phase shift measurement, allowing us to achieve 6.5 nm step sizes.

Moiré fringes of higher-order harmonics versus higher-order moiré patterns

This work presents a very simple and comprehensive approach for classification of the combinational spatial frequencies of the superimposed periodic or quasi-periodic structures. The reciprocal vectors of the structures are used to express their respective spectral components, and a unique reciprocal vectors equation is introduced for presenting the corresponding combinational frequencies. By the aid of the reciprocal vectors equation we classify moiré patterns of combinational frequencies into four classes: the conventional moiré pattern, moiré fringes of higher-order harmonics, higher-order moiré patterns, and pseudo-moiré patterns. The difference between the moiré fringes of higher-order harmonics and higher-order moiré patterns is expressed in the formulas. By some typical examples, conditions for simultaneous formation of moiré patterns of different harmonics of the superimposed gratings are investigated. We show that in the superimposition of two gratings, where at least one has a varying period and another has a non-sinusoidal profile, different moiré patterns are formed over different parts of the superimposed area, where a distinct pair of spatial frequencies of the superimposed structures contributes to the formation of each of the patterns. We use the same procedure in the analysis of simultaneously produced defected moiré patterns in the superimposition of a linear grating and a zone plate, where one or both consist of some topological defects at specific locations and at least one of the gratings has a non-sinusoidal profile. The topological defects of resulting moiré fringes are similar to those appearing in the interference patterns of optical vortices. It is shown that the defect number of resulting moiré fringes depends on the defect numbers and order of frequency harmonics of the gratings. The dependency of the defect number of the moiré fringes and its sign to the defect numbers of the gratings and their contributed frequency harmonics is derived for both additive and subtractive terms of moiré fringes, and the results are verified with several examples based on computational simulations.

Computerized interferometric surface measurements [Invited]

The addition of electronics, computers, and software to interferometry has enabled enormous improvements in optical metrology. This paper discusses four areas in which computerized interferometric measurement improvements have been made in the measurement of surface shape and surface roughness: (a) The use of computer-generated holograms for the testing of aspheric optics, (b) phase-shifting interferometry for getting interferometric data into a computer so the data can be analyzed, (c) computerized interference microscopes, including multiple-wavelength and coherence scanning, for the precision measurement of surface microstructure, and (d) vibration-insensitive dynamic interferometers for enabling precise measurements in noncontrolled environments.

Large-area Fabry-Perot modulator based on electro-optic polymers

We present a large-area electro-optic Fabry-Perot modulator utilizing a photoaddressable bis-azo polymer placed between two dielectric mirrors with an open aperture of 2 cm. A modulation efficiency of 1% at an effective modulation voltage of 20 V for a wavelength of 1.55 microm is demonstrated. By comparing distance tuning of the cavity with wavelength tuning, an effective electro-optic coefficient of -7 pm/V is measured.

Technical feasibility of figuring optical surfaces by ion polishing

Procedures are described to figure optical surfaces by ion polishing. Fused silica, ULE, and Cer-Vit were employed as substrate materials. The sputtering yields for these materials were: 1.9 (150-keV(40) Ar(+)), 1.86 (150-keV (40)Ar(+)), and 3.7 (80-keV (126)Xe(+)) atoms/ion, respectively. The optical scatter, at lambda = 632.8 nm, was measured to be 0.06%, which is comparable to good surfaces prepared by conventional lap techniques. The rms surface error was reduced from 0.05lambda to 0.01lambda over the central 0.12-m aperture of a 0.2-m diam fused silica flat by ion polishing with 150-keV (40)Ar(+). Based on this experience, the design of a manufacturing facility is discussed.