Short temporal coherence digital holography with a femtosecond frequency comb laser for multi-level optical sectioning

In this paper, we demonstrate how short temporal coherence digital holography with a femtosecond frequency comb laser source may be used for multi-level optical sectioning. The object shape is obtained by digitally reconstructing and processing a sequence of holograms recorded during stepwise shifting of a mirror in the reference arm. Experimental results are presented.

Digital holography of self-luminous objects by using a Mach-Zehnder setup

We describe a method where the wavefront emitted by a self-luminous object is superimposed to its filtered counterpart by using a Mach-Zehnder interferometer. The amplitude and phase of the resulting interference pattern is used for digital three-dimensional imaging. Experimental results are presented.

High-resolution quantitative phase microscopic imaging in deep UV with phase retrieval

High-resolution three-dimensional (3D) microscopic imaging requires the use of short wavelengths. Quantitative 3D imaging techniques, such as digital holographic microscopy, require interference between the object beam and a known reference background for the extraction of phase information. At shorter wavelengths, due to short coherence lengths, it may be difficult to implement a two-beam off-axis setup. Thus, a single-beam technique, which provides complete phase information, may be better suited for short wavelengths. This Letter describes the development of a quantitative microscopy technique at 193 nm using multiple intensity samplings and phase retrieval.

Phase retrieval by pinhole scanning

We describe a method where phase and amplitude of a wavefront are obtained by processing a sequence of pattern produced by the interference between the light transmitted by a scanning pinhole (which is sequentially shifted) and a reference pinhole. Simulations and experimental results are presented.

Resolution improvement in digital holography by angular and polarization multiplexing

Angular and polarization multiplexing techniques are utilized in both object and reference arms in the digital holographic microscopy system to improve its resolution. The angular multiplexing provides on-axis and off-axis illumination and reference beams with different carrier frequencies. Polarization multiplexing prohibits the occurrence of interference between low and high object spatial frequencies and reference beams. The proposed system does not require special light sources or filtering masks. Experimental results show that the resolution of the synthesized image exceeds the resolution determined by the numerical aperture of the imaging microscope objective.

Nanoscale imaging using deep ultraviolet digital holographic microscopy

A deep ultraviolet off-axis digital holographic microscope (DHM) is presented. The microscope has been arranged with as least as possible optical elements in the imaging path to avoid aberration due to the non-perfect optical elements. A high resolution approach has been implemented in the setup using oblique illumination to overcome the limitation introduced by the optical system. To examine the resolution of the system a nano-structured template has been designed and the result confirms the submicron and nanoscale resolution of the arranged DHM setup.

Phase microscopy of technical and biological samples through random phase modulation with a diffuser

A technique for phase microscopy using a phase diffuser and a reconstruction algorithm is proposed. A magnified specimen wavefront is projected on the diffuser plane that modulates the wavefront into a speckle field. The speckle patterns at axially displaced planes are sampled and used in an iterative phase retrieval algorithm based on a wave-propagation equation. The technique offers a whole-field and high-resolution wavefront reconstruction of unstained microstructures. Phase maps of photoresist targets and human cheek cells are obtained to demonstrate the effectiveness of our method.

Strategy for cryptanalysis of optical encryption in the Fresnel domain

Traditionally, cryptanalysis of optical security systems attempts to find original keys. Usually, by use of this kind of method, one can find a set of keys located close to the original keys in the key space. We call such a set the region of original key (ROK). For an optical encryption system in the Fresnel domain, such a strategy is ineffective since it needs to perform an exhaustive search to determine the system geometry or to solve an extremely large set of system equations. We propose to employ an alternative search strategy: to find a region of possible key (RPK). Since there is only one ROK for a cypher system but there are many RPKs, the probability to find a key in the RPK would be higher than in the ROK. Our analysis reveals that even a Fresnel-based encryption system has larger key space, but there are also serious security problems to be resolved.

Spiral phase filtering and orientation-selective edge detection/enhancement

A spiral phase plate with an azimuthal structure exp[iphi](0phi<2pi) has been used as a filter in a 4f system to achieve edge enhancement. Generally such edge-enhanced effect is isotropic, i.e., each edge of an input pattern is enhanced to the same degree regardless of its orientation. We found that one can achieve anisotropic edge enhancement by breaking down the symmetry of the filtering process. This can be done in two ways: first, by use of a fractional spiral phase filter (SPF) with a fractional topological charge and a controllable orientation of the edge discontinuity, and second, by the lateral shifting of the SPF. We interpret this process as a vortex formation due to the diffraction of the Fourier spectrum of the input pattern by a SPF with an integer and fractional topological charge. Optical experiments using a spatial light modulator were carried out to verify our proposal.

Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval

Shape and deformation measurement of diffusely reflecting 3D objects are very important in many application areas, including quality control, nondestructive testing, and design. When rough objects are exposed to coherent beams, the scattered light produces speckle fields. A method to measure the shape and deformation of 3D objects from the sequential intensity measurements of volume speckle field and phase retrieval based on angular-spectrum propagation technique is described here. The shape of a convex spherical surface was measured directly from the calculated phase map, and micrometer-sized deformation induced on a metal sheet was obtained upon subtraction of the phase, corresponding to unloaded and loaded states. Results from computer simulations confirm the experiments.

Angular displacement and deformation analyses using a speckle-based wavefront sensor

Wavefronts incident on a random phase plate are reconstructed via phase retrieval utilizing axially displaced speckle intensity measurements and the wave propagation equation. Retrieved phases and phase subtraction facilitate the investigations of wavefronts from test objects before and after undergoing a small rotation or deformation without sign ambiguity. Angular displacement (Deltatheta) between incident planar wavefronts is determined from the light source vacuum wavelength (lambda) divided by the fringe spacing (Lambda). Fourier analysis of the wavefront phase difference yields a peak frequency that is inversely proportional to Lambda, and the sign gives the direction of rotation. Numerical simulations confirm the experimental results. In the experiments, the smallest Deltatheta measured is 0.031 degrees . The technique also permits deformation analysis of a reflecting test object under thermal loading. The technique offers simple, high resolution, noncontact, and whole field evaluation of three-dimensional objects before and after undergoing rotation or deformation.

Real-time extended dynamic range imaging in shearography

Extended dynamic range (EDR) imaging is a postprocessing technique commonly associated with photography. Multiple images of a scene are recorded by the camera using different shutter settings and are merged into a single higher dynamic range image. Speckle interferometry and holography techniques require a well-modulated intensity signal to extract the phase information, and of these techniques shearography is most sensitive to different object surface reflectivities as it uses self-referencing from a sheared image. In this paper the authors demonstrate real-time EDR imaging in shearography and present experimental results from a difficult surface reflectivity sample: a wooden panel painting containing gold and dark earth color paint.

Coherence effects in digital in-line holographic microscopy

We analyze the effects of partial coherence in the image formation of a digital in-line holographic microscope (DIHM). The impulse response is described as a function of cross-spectral density of the light used in the space-frequency domain. Numerical simulation based on the applied model shows that a reduction in coherence of light leads to broadening of the impulse response. This is also validated by results from experiments wherein a DIHM is used to image latex beads using light with different spatial and temporal coherence.

Interferometric evaluation of angular displacements using phase retrieval

Phase retrieval is carried out using sequential intensity measurements of a volume speckle field and a wave propagation equation. Retrieved phases and phase subtraction facilitate the analysis of wavefronts before and after undergoing a small rotation. Angular displacement between incident planar wavefronts is determined from the unwrapped phase difference, phase diffuser aperture diameter, and the light source wavelength. Numerical simulations confirm the experimental results.

Phase retrieval of complex optical fields by binary amplitude modulation

A method to retrieve the complex optical fields from the intensity information recorded in only one plane is discussed. The wavefront to be reconstructed is modulated by using a random binary amplitude mask. Wavefronts with a rather large phase depth can be accurately retrieved by using several masks in combination with iterative Fresnel algorithms and without any prior information. The influences of the contrast of the mask and the dynamic range of the detector on the accuracy of the phase retrieval are analyzed.

High-fidelity numerical realization of multiple-step Fresnel propagation for the reconstruction of digital holograms

A cascaded Fresnel algorithm for the flexible reconstruction of digital holograms is proposed. Since the fast-Fourier-transform-based numerical realization of the Fresnel integral shows a dependency of its pixel resolution and its computation window size on the propagation distance different from that of the corresponding physical system, the computation window can be smaller than the actual physical diffraction field in the intermediate plane. Consequently, distortions in the final reconstruction may occur. A method is proposed to eliminate such distortion. The validity of this method is shown by both numerical simulations and experimental results.

Phase retrieval using multiple illumination wavelengths

An iterative phase retrieval method is proposed, which uses a sequence of diffraction intensity patterns recorded at different wavelengths. This method has a rapid convergence, and a high immunity to noise and environmental disturbance. The wrap-free phase measurement range is also extended based on the principle of two-wavelength interferometry. Simulation and experimental results are presented to demonstrate the approach.

Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence

In recent years, optical interferometry has been applied to the whole-field, noncontact measurement of vibrating or continuously deforming objects. In many cases, a high resolution measurement of kinematic (displacement, velocity, and acceleration, etc.) and deformation parameters (strain, curvature, and twist, etc.) can give useful information on the dynamic response of the objects concerned. Different signal processing algorithms are applied to two types of interferogram sequences, which were captured by a high-speed camera using different interferometric setups: (1) a speckle or fringe pattern sequence with a temporal carrier and (2) a wrapped phase map sequence. These algorithms include Fourier transform, windowed Fourier transform, wavelet transform, and even a combination of two of these techniques. We will compare these algorithms using the example of a 1D temporal evaluation of interferogram sequences and extend these algorithms to 2D and 3D processing, so that accurate kinematic and deformation parameters of moving objects can be evaluated with different types of optical interferometry.

Digital holographic microscopy in the deep (193 nm) ultraviolet

We present a system based on digital holography suitable for the investigation of microscopic objects. To increase the resolution of the system a deep (193 nm) UV laser source has been used. A method for compensating aberrations due to the non-perfect optical elements used for the recording has been developed. The system allows the investigation of reflecting and transmitting samples.

Vibration measurement by temporal Fourier analyses of a digital hologram sequence

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.

Three-dimensional angle measurement based on propagation vector analysis of digital holography

We propose what we believe to be a novel method for highly accurate three-dimensional (3D) angle measurement based on propagation vector analysis of digital holography. Three-dimensional rotations in space can be achieved by use of a CCD camera and a multifacet object, which reflects an incident wave into different directions. The propagation vectors of the reflected waves from the object can be extracted by analyzing the object spectrum of the recorded hologram. Any small rotation of the object will induce a change in the propagation vectors in space, which can then be used for 3D angle measurement. Experimental results are presented to verify the idea.

Wavefront sensing with random amplitude mask and phase retrieval

A light beam with an ideal wavefront that is transmitted or reflected from an object is modified by different characteristics of the object such as shape, refractive index, density, or temperature. Wavefront sensing therefore yields valuable information about the system or the changes happening to the system. A new method for wavefront sensing using a random amplitude mask and a phase retrieval method based on the Rayleigh-Sommerfeld wave propagation equation is described. The proposed method has many potential applications ranging from phase contrast imaging and measurement of lens aberration to shape measurement of three-dimensional objects.

Aperture synthesis in phase retrieval using a volume-speckle field

The resolution of the reconstructed wave by a phase-retrieval method using a volume-speckle field depends on the aperture defined by the size of the CCD array. The use of a larger aperture is introduced by measuring the speckle field at two different positions in the transverse plane and stitching the measurements together. Improvements in the quality of reconstructions are demonstrated experimentally and by computer simulations. Undesirable effects of camera tilt on the quality of reconstructions from synthetic aperture intensity measurements are experimentally observed and corrected.

Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field

The recording of the volume speckle field from an object at different planes combined with the wave propagation equation allows the reconstruction of the wavefront 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 because no reference wave is required as in the case of holography. The phase retrieval technique is applied to the investigation of diffusely transmitting and reflecting objects. The effects of different parameters on the quality of reconstructions are investigated by simulation and experiment. Significant enhancements of the reconstructions 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 reconstruction. The results from computer simulations confirm the experiments. Analysis of transverse and longitudinal intensity distributions of a volume speckle field for the SBMIR technique is presented. Enhancing the resolution method by shifting the camera a distance of a half-pixel in the lateral direction improves the sampling of speckle patterns and leads to better quality reconstructions. This allows the possibility of recording wave fields from larger test objects.