RESUMEN
Optical areal profilometry of large precision-engineered surfaces require high-resolution measurements over large fields of view. Synthetic Aperture Interferometry (SAI) offers an alternative to the conventional approach of stitching small fields of view (FOV) obtained with Coherent Scanning Interferometry (CSI) using high-NA objectives. In SAI, low-resolution digital holograms are recorded for different illumination and observation directions and they are added coherently to produce a high-resolution reconstruction over a large FOV. This paper describes the design, fabrication and characterization of a large FOV, compact and low-cost coherent imager (CI) as a building block of a coherent sensor array for a SAI system. The CI consists of a CMOS photodetector array with 1.12 µm pixel pitch, a square entrance pupil and a highly divergent reference beam that emerges from a pinhole milled with a focused ion beam on the cylindrical cladding at the tip of an optical fibre. In order to accurately reconstruct the digital holograms, the wavefront of the reference beam is estimated by localizing the reference source relative to the photodetector array. This is done using an optimization approach that simultaneously reconstructs plane waves that reach the aperture from 121 different illumination directions and guarantees a phase root-mean-squared (RMS) error of less than a fifth of the wavelength across the CI entrance pupil at a boundary of the FOV. The CI performance is demonstrated with a holographic reconstruction of a 0.110 m wide object placed at a distance of 0.085 m, i.e. a FOV = ±0.57â rad, the highest reported to date with a holographic camera.
RESUMEN
A hologram is a recording of the interference between an unknown object wave and a coherent reference wave. Providing the object and reference waves are sufficiently separated in some region of space and the reference beam is known, a high-fidelity reconstruction of the object wave is possible. In traditional optical holography, high-quality reconstruction is achieved by careful reillumination of the holographic plate with the exact same reference wave that was used at the recording stage. To reconstruct high-quality digital holograms the exact parameters of the reference wave must be known mathematically. This paper discusses a technique that obtains the mathematical parameters that characterize a strongly divergent reference wave that originates from a fiber source in a new compact digital holographic camera. This is a lensless design that is similar in principle to a Fourier hologram, but because of the large numerical aperture, the usual paraxial approximations cannot be applied and the Fourier relationship is inexact. To characterize the reference wave, recordings of quasi-planar object waves are made at various angles of incidence using a Dammann grating. An optimization process is then used to find the reference wave that reconstructs a stigmatic image of the object wave regardless of the angle of incidence.
RESUMEN
We present results from numerical simulations of a dynamic phase-shifting speckle interferometer used in the presence of mechanical vibrations. The simulation is based on a detailed mathematical model of the system, which is used to predict the expected frequency response of the rms measurement error, in the time-varying phase difference maps, as a result of vibration. The performance of different phase-shifting algorithms is studied over a range of vibrational frequencies. Phase-difference evaluation is performed by means of temporal phase shifting and temporal phase unwrapping. It is demonstrated that longer sampling windows and higher framing rates are preferred in order to reduce the phase-change error that is due to vibration. A numerical criterion for an upper limit on the length of time window for the phase-shifting algorithm is also proposed. The numerical results are finally compared with experimental data, acquired with a phase-shifting speckle interferometer of 1000 frames/s.