In this paper a single-shot digital holographic set-up with two orthogonally polarized reference beams is proposed to achieve rapid acquisition of Magneto-Optical Kerr Effect images. Principles of the method and the background theory for dynamic state of polarization measurement by use of digital holography are presented. This system has no mechanically moving elements or active elements for polarization control and modulation. An object beam is combined with two reference beams at different off-axis angles and is guided to a detector. Then two complex fields (interference terms) representing two orthogonal polarizations are recorded in a single frame simultaneously. Thereafter the complex fields are numerically reconstructed and carrier frequency calibration is done to remove aberrations introduced in multiplexed digital holographic recordings. From the numerical values of amplitude and phase, a real time quantitative analysis of the polarization state is possible by use of Jones vectors. The technique is demonstrated on a magnetic sample that is a lithographically patterned magnetic microstructure consisting of thin permalloy parallel stripes.
In an on line shape measurement in disturbed environment, use of many wavelengths in order to avoid
phase ambiguity may become a problem as it is necessary to acquire all holograms simultaneously due to environmental
disturbances. Therefore to make the shape data available the different holograms have to be extracted from a single
recorded image in spectral domain. Appropriate cut areas in the Fourier method are therefore of great importance for
decoding information carried by different wavelengths. Furthermore using different laser sources, induces aberration and
pseudo phase changes which must be compensated. To insure any phase change is only because of the object shape,
calibration is therefore indispensable. For this purpose, effects of uncontrolled carrier frequency filtering are discussed.
A registration procedure is applied using minimum speckle displacements to find the best cut area to extract and match
the interference terms. Both holograms are numerically propagated to a focus plane to avoid any unknown errors.
Deviations between a reference known plate and its measurement are found and used for calibration. We demonstrate
that phase maps and speckle displacements can be recovered free of chromatic aberrations. To our knowledge, this is the
first time that a single shot dual wavelength calibration is reported by defining a criteria to make the spatial filtering
automatic avoiding the problems of manual methods. The procedure is shown to give shape accuracy of 35μm with
negligible systematic errors using a synthetic wavelength of 1.1 mm.
A new method to measure shape by analyzing the speckle movements in images generated by numerical propagation from dual-wavelength holograms is presented. The relationship of the speckle movements at different focal distances is formulated, and it is shown how this carries information about the surface position as well as the local slope of the object. It is experimentally verified that dual-wavelength holography and numerically generated speckle images can be used together with digital speckle correlation to retrieve the object shape. From a measurement on a cylindrical test object, the method is demonstrated to have a random error in the order of a few micrometers.
A new technique to measure depth based on dual wavelength digital holography and image correlation of speckle
movements is demonstrated. By numerical refocusing of the complex optical field to different focus planes and by
measuring the speckle movements caused by a wavelength shift both the object surface position and its local slope can
be determined. It is shown how the speckle movement varies linearly with the surface slope, the wavelength shift and the
distance of the numerical propagation. This gives a possibility to measure the slope with approximately the same
precision as from the interferometric phase maps. In addition, when the object surface is in focus there is no speckle
movement so by estimating in what plane the speckle movement is zero the absolute surface position can be measured.
The objective of this paper is to discuss the properties and a few applications of multi-spectral speckles. The paper starts with a theoretical section where the correlation properties of multi-spectral speckles are detailed for the case of reflective imaging geometry. Both a free-space geometry and an imaging geometry are detailed. As an application example effects and possibilities provided by the theory in a measurement of surface shape of a generally shaped object from a dual-wavelength holographic recording are detailed. It is showed that the same phase profile is obtained from integration of speckle movements and phase unwrapping and they are therefore exchangeable quantities.
When measuring 3D-shape with triangulation and projected interference fringes it is of interest to reduce the phase error
in the fringe pattern. A study has been carried out concerning parameters that will affect the phase error and an analytical
expression has been derived. It is concluded that the phase error depends on the speckle contrast, C, and the modulation,
M, of the fringes and since the phase in this investigation is determined using the spatial carrier method the phase error
also depends on the filtering of the Fourier spectrum. To reduce the phase error this work has been focusing on
suppressing the speckle contrast. For this the method with a moving aperture is used; a disk with several apertures is
rotated in the aperture plane of the camera lens. To verify the derived expression for the phase error and the method to
suppress speckles both numerical simulations and experiments have been performed. In the measurements made it was
concluded that after an aperture movement of three aperture diameters the speckle contrast and hence the phase error was
reduced by 60 %. A phase error of 0.15 radians was obtained in the experiments, thus approximately 1/40 of a fringe
period.
Decorrelation in an interferometric set-up appears due to movements of the speckle pattern. In the case of rigid body
movements the effect of decorrelation severely limits the performance of speckle interferometers. If the movement is
larger than the speckle size the wanted phase information of the deformation is lost.
Phase modulating spatial light modulators (SLMs) provide a new method to non-mechanically deflect and shape light.
By using the SLM for scanning the field-of-view and focusing at different distances it is possible to measure intensity
speckle patterns in a three-dimensional volume. These intensity images can then be cross correlated to give a three-dimensional
correlation coefficient of the speckle pattern.
If an SLM is utilized in an interferometric set-up it is possible to compensate for unwanted movements during an
experiment. The measured correlation coefficient will then provide information regarding how large movements that are
allowed with maintained performance of the interferometer. It is shown that for large movements the SLM can be used to
retrieve phase maps.
A novel retrocommunication link utilizing reflective multiple quantum well (MQW) optical modulators and nonmechanical beam steering and tracking is demonstrated. Large aperture reflective MQW modulators using AlGaAs/GaAs are optimized and manufactured. The modulators exhibit a contrast ratio larger than 4:1 and a modulation bandwidth of 10 MHz. Nonmechanical beam steering and tracking are studied using nematic liquid crystal (NLC) spatial light modulators (SLMs). The communication link is comprised of a retromodulating array with four MQW modulators and a transceiver using a NLC SLM for beam steering and tracking. Transfer of audio, real-time image data and pseudorandom bit sequences over 100-m range while tracking the moving retromodulator is shown. The link is capable of transferring data at approximately 8 Mbps.
Retrocommunication is a new technique for asymmetric free-space optical communication that has attracted interest during recent years. Novel technologies such as multiple quantum well (MQW) optical modulators and non-mechanical laser beam steering and tracking have been studied for implementation in a retrocommunication link. Large and small aperture reflective AlGaAs/GaAs MQW modulators were optimised and fabricated. The modulators exhibit high contrast ratios (from 5 to 100) and high modulation rates (up to 16 Mbit/s). A retroreceiver consisting of four large aperture MQW modulators, associated optics and drive electronics was fabricated. Nematic liquid crystal spatial light modulators have been evaluated, characterised for beam steering and tracking and implemented in a transceiver. Small area MQW modulators, used in focal plane configurations, were studied for static communication links. Results from a novel retrocommunication link utilising a retroreceiver and non-mechanical laser beam steering and tracking will be presented. Bit rates of 8 Mbit/s were observed during non-mechanical tracking of a moving retroreceiver over 100 m range. The demonstrator system was capable of transferring audio-, real-time images or bit streams. The demonstrated principles show promising features for future low weight free-space communication links. Performance calculations including requirements for a retrocommunication link using MQW modulators and non-mechanical beam steering are discussed.
The polarization properties of a one-dimensional, 1x4096 pixels, zero-twist nematic liquid crystal (NLC) spatial light modulator (SLM) were investigated. The fringing electric field between pixels can introduce twist deformations in addition to the wanted splay and bend. The twist will affect the polarization and couple energy between polarization modes. The electric fields and director distribution in the LC were numerically determined by solving a set of coupled partial differential equations. The optical propagation in the resulting inhomogeneous anisotropic crystal was performed by the finite-difference time-domain (FDTD) method. The simulated results were validated by comparison with experimental diffraction patterns. As the numerical scheme is slow a simple semi-empirical model was also developed. Using parameters from the simulated results the model was adjusted to allow rapid calculations of the polarization distribution of the light modulated by the SLM.
A commercial linear one-dimensional, 1x4096 pixels, zero-twist nematic liquid crystal spatial light modulator (SLM), giving more than 2π phase modulation at λ = 850 nm, was evaluated for beam steering applications. The large ratio (7:1) between the liquid crystal layer thickness and pixel width gives rise to voltage leakage and fringing fields between pixels. Due to the fringing fields the ideal calculated phase patterns cannot be perfectly realized by the device. Losses in high frequency components in the phase patterns were found to limit the maximum deflection angle. The inhomogeneous optical anisotropy of the SLM was determined by modelling of the liquid crystal director distribution within the electrode-pixel structure. The effects of the fringing fields on the amplitude and phase modulation were studied by full vector finite-difference time-domain simulations. It was found that the fringing fields also resulted in coupling into an unwanted polarization mode. Measurements of how this mode coupling affects the beam steering quality were carried out and the results compared with calculated results. A method to compensate for the fringing field effects is discussed and it is shown how the usable steering range of the SLM can be extended to ± 2 degrees.
A linear one-dimensional, 1x4096 pixel, zero-twist nematic liquid crystal spatial light modulator (SLM) was evaluated for laser beam steering and tracking applications. The commercially obtained SLM is designed to operate at, λ = 850 nm, allowing more than 2 π phase modulation. Due to voltage leakage the phase modulation experienced by the wave front differed from the ideal calculated phase patterns. This cross talk between pixels reduces the diffraction efficiency. Different methods developed to compensate for this effect are presented. The usable steering range of the SLM was extended to ± 2 degrees using improved phase patterns. A simple model was developed to simulate the optical effects of the voltage leakage. Preliminary tracking experiments were carried out in a laboratory set-up using a moving corner cube retro reflector. The beam steering SLM was implemented in a transceiver for free-space optical communication. Initial results using the transceiver up to 180 m range are presented.
The spatial light modulator (SLM) can be used to alter the phase of the wave front to achieve a deflection or a change in the shape of a laser beam. In this study a commercial nematic zero-twist liquid crystal SLM was evaluated. SLMs can be operated to produce pure phase modulation necessary for beam steering. For liquid crystals the relation between applied voltage and phase modulation is highly non-linear due to the relation between the voltage driven molecular tilt angle and extraordinary refractive index. To compensate for this effect we optimized and examined look-up tables (LUT) that realize the inverse of the phase response. It was found that the factory LUT improved the power ratio between the zero order and the first order peaks five times compared to the case without using an LUT, however, further improvement of this ratio of two was reached using an LUT optimized from the measured phase response of the SLM. The discrete phase modulation results in a stepped, non-ideal blazed grating that alters the relative power of the available steering angles. To obtain optimal performance these effects must be analyzed for different bit depths and preliminary results of such quantization effects are discussed.
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