From speckle pattern photography to digital holographic interferometry [Invited].

Speckles are inherently an interference phenomenon produced when an optically rough surface or a turbulent medium introduces some degree of randomness to a reflected or a transmitted electromagnetic field. Speckles are often nuisance in coherent image formation. Speckle patterns are however a useful tool for displacement and deformation as well as vibration and stress analysis. The development of speckle photography to speckle interferometry and digital holographic interferometry is described in this paper.

Time-resolved vibration measurement with temporal speckle pattern interferometry.

Temporal speckle pattern interferometry (TSPI) is an optical measurement procedurefor measuring the displacement of rough technical surfaces. The time-dependent speckle modulation due to optical path difference changes is tracked during the whole displacement of the surface and then evaluated pointwise without referring to neighboring pixels. This feature allows for its use as independent point sensors. This aspect of incremental phase tracking enables TSPI to be used to measure time-resolved mechanical vibrations. It also reduces the deteriorating effect of the decorrelation. Therefore large displacements can be measured. A concept for an inexpensive fiber-optical point sensor was developed and the theoretical accuracy for vibration measurement was investigated. The TSPI measurement of a loudspeaker membrane is compared with a high-precision vibrometer measurement. The first results show good agreement.

Fast digital hologram generation and adaptive force measurement in liquid-crystal-display-based holographic tweezers.

Computer-generated holograms in conjunction with spatial light modulators (SLMs) offer a way to dynamically generate holograms that are adapted to specific tasks. To use the full dynamic capability of the SLM, the hologram computation should be very fast. We present a method that uses the highly parallel architecture of a consumer graphics board to compute analytical holograms in video real time. A precice characterization of the SLM (Holoeye LC-R-2500) and the adaption of its settings to our near-infrared application is necessary to guarantee an efficient hologram reconstruction. The benefits of a fast computation of adapted holograms and the application of an efficient SLM are demonstrated by measuring the trapping forces of holographic tweezers.

Diffraction-induced coherence levels.

We examined the influence of complex diffraction effects on low-coherence fringes created for high-aspect depth-to-width ratio structures called trenches. The coherence function was analyzed for these micrometer-wide trenches and was registered with a white-light interference microscope. For some types of surface structure we observed that additional low-coherence fringes that do not correspond directly to the surface topology are formed near the sharp edges of the structures. These additional coherence fringes were studied by rigorous numerical evaluations of vector diffractions, and these simulated interference fields were then compared with experimental results that were obtained with a white-light interference microscope.

Reconstruction of in-line digital holograms from two intensity measurements.

We propose a new method based on in-line digital holography for the reconstruction of a wave front from only two intensity recordings. The simulation result shows that this method works well when the object wave is weak compared with the reference wave. This technique can be employed for real-time imaging.

Applications of fractional transforms to object reconstruction from in-line holograms.

We propose a method for the digital reconstruction of an object whose diffraction pattern has been recorded on a hologram. The fractional Fourier transform is used for the object reconstruction. To determine the position of the object, the fractional order is scanned. The fractional cosine and fractional Hartley transforms are also employed for object reconstruction. These two transforms are real valued and allow the reconstruction to be done with lower computing complexity. Simulations and experimental results are presented.

Image reconstruction for in-line holography with the Yang-Gu algorithm.

A new approach to the numerical reconstruction of wave fronts stored by in-line holography is presented. The new algorithm can achieve good reconstructed results in both unitary and nonunitary systems. The influences of recording distance and noise as well as of digitalization errors on the quality of reconstruction are numerically investigated. The experimental results demonstrate the validity of this new approach.

Temporal phase unwrapping of digital hologram sequences.

A method for recording and evaluating digital image-plane holograms is presented. Hundreds of holograms of an object that has been subjected to dynamic deformation (e.g., vibrations) are recorded. The phase of the wave front is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. By temporal phase unwrapping it is possible to determine the absolute deformation (included the direction of motion) of the object. Experimental results are presented, and the advantages of temporal phase unwrapping compared with spatial phase unwrapping are discussed.

Absolute interferometric test of aspheres by use of twin computer-generated holograms.

A complete absolute interferometric test of axially symmetric aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The aberrations of the spherical auxiliary wave are measured absolutely with either a spherical mirror or an absolute test for Fresnel zone plates. Thus the two types of aberration inherent in the CGH can be identified and separated from each other. The errors of the spherical wave can be transferred to those of the aspherical wave. Two different methods thatuse Twin-CGHs for absolute testing of aspheric surfaces are described. Test procedures are explained, equations are derived, and experimental results are presented. A mutual comparison of the two results and a comparison with the established N-position rotation test are given.

Microscopic three-dimensional topometry with ferroelectric liquid-crystal-on-silicon displays.

When three dimensional measurements are conducted with fringe projection, the quality of the grating used for the generation of the fringes is important. It has a direct influence on the achievable depth resolution in a given measurement setup. In the past, Ronchi grating or gratings written in nematic liquid-crystal displays or in digital micromirror devices have been used. We report on the application of a reflective ferroelectric liquid-crystal-on-silicon display as the fringe-generating element in a setup based on a stereo microscope. With this device the depth resolution of measurements by use of phase-shifting algorithms can be significantly improved compared with the application of a Ronchi grating or a nematic liquid-crystal display.

Non-mechanically-axial-scanning confocal microscope using adaptive mirror switching.

A non-axial-scanning confocal microscope employing a monochromatic light source has been developed. The system controls the defocus of an objective into three to .ve optimized states by using a membrane-adaptive mirror, and determines the axial height of an object according to the confocal output value with each defocus. A genetic algorithm is employed to optimize the adaptive mirror shape, with the information entropy of the spectrum of the lateral confocal spot pro.le used as a cost function in the genetic algorithm. Our experimental system successfully determined axial object height within 50 microm range with 0.64 % of error.

Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm.

The phase retrieval algorithm has been used in this paper for whole reconstruction of the optical wave fields. The quantitative information of the phase distribution as well as the intensity distribution of the reconstruction field at different locations along the propagation direction has been achieved from double or multi in-line holograms. Numerical reconstructions of the wave fields from experimentally recorded in-line holograms are presented. This technique can be potentially applied for aberrated wave front analyzing and 3D imaging.

Short-coherence digital microscopy by use of a lensless holographic imaging system.

An optical system based on short-coherence digital holography suitable for three-dimensional (3D) microscopic investigations is described. The light source is a short-coherence laser, and the holograms are recorded on a CCD sensor. The interference (hologram) occurs only when the path lengths of the reference and the object beam are matched within the coherence length of the laser. The image of the part of the sample that matches the reference beam is reconstructed by numerical evaluation of the hologram. The advantages of the method are high numerical aperture (this means high spatial resolution), detection of the 3D shape, and a lensless imaging system. Experimental results are presented.

Digital-holographic interferometry with an image-intensifier system.

A method for recording digital holograms on an image intensifier coupled with a CCD sensor is presented. The advantage of the image intensifier is that it can be gated (electronic shutter action produced by controlling of the image intensifier's photocathode voltage). This allows us to record holograms with a short exposure time. Two holograms of an object submitted to dynamical displacements (e.g., vibrations) are recorded by two short exposures. The phase of the wave front recorded at different times is calculated from the recorded intensity by use of a digital Fourier-transform method. By comparison of the phases recorded it is possible to get the displacement of the object during a short interval. Experimental results are presented, and the problems related to the noise and to the spatial resolution are discussed.

Enhancement of the dynamic range of the detected intensity in an optical measurement system by a three-channel technique.

When three-dimensional optical topometry of technical surfaces is performed, one major problem is that often the local reflectance of the object's surface varies within a wide range. This leads to overexposed and underexposed areas on the detector, where no measurements can be made. To overcome this problem, we have developed a method that extends the dynamic range of an imaging system. As an example we implemented this method to a measurement system that is based on fringe projection with a data projector and a color CCD camera. By projection of quasi-monochromatic fringes a different dynamic range in each of the three color channels of the camera is achieved. Hence the overall dynamic range of the system is increased by a factor larger than 5.