Previous implementations of the phase diffuser used in the multiple-plane phase retrieval method included a diffuser glass plate with fixed optical properties or a programmable yet expensive spatial light modulator. Here a model for phase retrieval based on a digital micromirror device as amplitude diffuser is presented. The technique offers programmable, convenient and low-cost amplitude diffuser for a non-stagnating iterative phase retrieval. The technique is demonstrated in the reconstructions of smooth object wavefronts.
Speckle noise presents challenges in object localization using reconstructed wavefronts. Here, a technique for axial localization of rough test objects based on a statistical algorithm that processes volume speckle fields is demonstrated numerically and experimentally. The algorithm utilizes the standard deviation of phase difference maps as a metric to characterize the object wavefront at different axial locations. Compared with an amplitude-based localization method utilizing energy of image gradient, the technique is shown to be robust against speckle noise.
Fringe patterns carry valuable spatio-temporal information about the object being investigated. Fringe processing, however, is hampered by the presence of speckle noise which is a by-product of coherent metrology of optically rough surfaces. A speckle noise-robust fringe processing algorithm we developed based on the statistical properties of fringe patterns is revisited. The algorithm evaluates the change in the standard deviation of fringe patterns yielding a 2-D contrast map of spatial frequencies along the transverse directions. Application of the algorithm along the axial direction has not been reported. Here a technique for enhanced axial localization of rough test objects based on the statistical fringe processing algorithm is demonstrated experimentally. The main advantages of the localization technique are robustness against speckle noise and high axial resolution in the range of the light source wavelength.
A technique for the localization of 3-D refractive test objects is presented. It uses the statistical behavior of axially propagated wavefronts as a metric to determine object location. The wavefront is obtained using digital holography. The wavefront phase is plotted at equally-spaced axial planes within the wavelength of the light source used. For each transverse phase plot, standard deviation (SD) values are obtained. The axial variation of the SD values yield a contrast map showing the spatial features of the wavefront. To locate the test object along the axial direction, the contrast maps are correlated to a Gaussian test function. The test phase objects objects are transparent adhesive films placed on opposite sides of a 1-mm thick glass slide. This is then mounted approximately 77 mm from the camera plane. Using the proposed technique, the axial distance between the transparent films was determined to be 1.0112mm which indicates the glass slide thickness. The correlation plot yields a well-behaved curve facilitating the precise localization of the test objects.
For deterministic phase retrieval, the problem of insignificant axial intensity variations upon defocus of a smooth object
wavefront is addressed. Our proposed solution is based on the use of a phase diffuser facilitating the formation of a
partially-developed speckle field (i.e., a field with both scattered-wave and unperturbed-wave components). The smooth
test wavefront impinges first on the phase diffuser producing the speckle field. Then two speckle patterns with different
defocus are recorded at the output plane of a 4f-optical filtering setup with a spatial light modulator (SLM) in the
common Fourier domain. The local variations of the recorded speckle patterns and the defocus distance approximate the
axial intensity derivative which, in turn, is required to recover the wavefront phase via the transport of intensity equation
(TIE). The SLM setup reduces the speckle recording time and the TIE allows direct (i.e., non-iterative) calculation of the
phase. The pre-requisite partially-developed speckle field in our technique facilitates high image contrast and significant
axial intensity variation. Wavefront reconstruction for the 3D refractive test object used demonstrates the effectiveness
of the technique.
Complete laser wavefront, with phase and intensity, is digitally reconstructed using a speckle-based phase retrieval
method. An automated technique for the full characterization of a laser beam focus and the correction for astigmatism
due to lens rotational misalignment is presented. The technique is also demonstrated in the corrections for illumination
beam tilt and lens defocus in the imaging of the high spatial frequency content in phase objects. The proposed wavefront
alignment technique is fast, precise and robust against aberrations.
Digital shearography is an optical technique that allows direct measurement of strain in deforming samples and
detection of surface and sub-surface defects. Because of its simple set-up and insensitivity to rigid body translations,
the method has gained considerable importance in nondestructive testing in an industrial environment. Despite of its
advantages, however, its application remains limited to highly scattering opaque samples due to its high dependence on
the quality of speckles. This study demonstrates the suitability of digital shearography in the strain analysis of acrylic
glass, a transparent sample, under sub-surface compaction loading. To generate the speckles, nominal roughness is
induced at the front surface of the glass. As compared to the polariscope, digital shearography is shown to be able to
resolve microscopic displacements that may not be evident as birefringence. Microscopic strain induced in the
sample in the order of 60 microstrains is resolved using the shearographic set-up. For a more complete investigation of
the deformation in the sample, the sub-surface displacements in the material are also mapped using Fourier digital
holography to complement the shearographic results. The technique can be applied to fluid flow visualization and
evaluation of polymers and other transparent materials.
A setup for the simultaneous recording of axially-displaced intensity patterns of a volume speckle field to be used for
phase retrieval is proposed. Beam splitters (BS) are cascaded directing the beams to different detectors, in turn,
generating different sampling planes. The effective power, which is reflected in the speckle intensity measurements, is
however compromised. The BS's transmission and reflection coefficients are evaluated according to the setup under the
assumption that the only power loss induced is due to these optics. Simulations show a set of BS combination that
delivers the same beam intensity of at least 6% to all the planes still results in successful phase retrieval. Other
combinations of beam splitter transmission and reflection values are also explored. The single-shot operation of the
proposed technique avoids the time-consuming sequential measurements of the speckle field. Possible future studies
include application of the technique to measure a system's characteristic properties that are not temporally fixed like
temperature and optical turbulence in the environment.
Wavefront curvature sensing with phase error correction system is carried out using phase retrieval based on a partially-developed
volume speckle field. Various wavefronts are reconstructed: planar, spherical, cylindrical, and a wavefront
passing through the side of a bare optical fiber. Spurious fringe pattern in the reconstructions due to a small tilt in the
plane illumination wave is detected and numerically corrected for. Difference in the curvatures of two spherical
wavefronts is also evaluated. Possible applications include angular displacement and range measurements.
3D imaging of wavefronts for the characterization of an object with which it interacts is an interesting and challenging
problem. Wavefront sensing or the measurement of the deviations from an ideal wavefront yields valuable information
of the object under study such as refractive index distribution, density distribution and temperature profile. Traditional
phase reconstruction methods like holography involves a complicated setup and procedure and methods based on the
Shack-Hartmann sensor have poor spatial resolution. In this study, an alternative wavefront sensor based on a phase
retrieval method and a random amplitude mask is proposed. The main advantages of the proposed wavefront sensor are
high resolution in the order of a few microns, accurate and fast-convergent phase reconstruction and a simple setup. The
principles of the technique and the algorithm of the phase retrieval method are described in detail. The functions of the
main components of the proposed sensor which include a mask, an imaging sensor and a computerized phase retrieval
algorithm are also discussed. The dependences of the accuracy of the phase reconstructions on the number of intensity
recordings and iterations are investigated. It was observed that about 16 intensity recordings and 5-7 iterations are
sufficient to obtain a convergence between the calculated phase and the true phase. An initial random guess phase was
also found to result in a faster rate of convergence as compared to an initial constant guess phase. Experimental
implementation the proposed wavefront sensor is demonstrated.
The recording of the volume speckle field from an object at different planes, combined with the wave propagation equation allows the reconstruction of the wave front phase and amplitude without requiring a reference wave. The main advantage of this single-beam multiple-intensity reconstruction (SBMIR) technique is the simple experimental setup due to the fact that no reference wave is required as it is in the case of holography. In this study the method is applied to the investigations of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions were investigated by simulation and experiment. Significant improvements are observed when the number of intensity measurements is 15 or more and the sequential measurement distance is 0.5 mm or larger. Performing two iterations during the reconstruction process using the calculated phase also leads to better reconstructions. The results from simulation and experiments agreed well. Subsequent work has shown that super image methods like shifting the camera a distance of half-pixel in the lateral directions enhance the sampling of speckle patterns and lead to better reconstructions. This allows to the possibility of recording wave fields from larger test objects.