Correlation optics provides tools—both conceptual and experimental—for measuring various parameters of an optical field in partial coherence and polarization. This area of study could enable unique applications for industrial quality control, solid-state physics, medical diagnostics and ecological monitoring.
One of the most important concepts in optics is coherence. Initial investigations by Thomas Young and Augustin Fresnel linked coherence with the notion of polarization in the early 1800s. Over the years, many investigators have explored coherence and polarization, and scientists’ interest in these areas has grown steadily over the past 20 years.
It is common knowledge that completely coherent and completely incoherent light—as well as completely polarized and completely unpolarized light—does not exist. Real light is always partially coherent and partially polarized. Before the formation of the modern theory on partial coherence and partial polarization and prior to the invention of the laser, scientists would make theoretical measurements in which they added mutually incoherent beams in intensity and mutually coherent beams in complex amplitudes. However, these measurements are not physically possible in the real world.
While it’s easy to distinguish between coherence and polarization in theoretical experiments, in practical applications the two phenomena are interconnected. This understanding has led to the formation of a new field of optics and photonics: correlation optics.
Correlation optics is the study of the statistical wave optics of partially coherent and partially polarized light fields described in terms of correlation functions as the second-order statistical moments of various field parameters. It measures statistical accordance but does not define the actual cause-effect relationship between two or more variables.
Researchers in this field aim to establish interconnections between correlation parameters of a light field scattered by an object and the statistical characteristics of that object. Their work has led to the development of new metrological tools for performing optical diagnostics of light-scattering objects and media, and to experimental solutions of the inverse problems in optics. Correlation optics techniques can also be used to interpret many optical phenomena, ranging from holographic associative memories to induced spectral changes of polychromatic radiation.
Applications of correlation optics
Holography is a handy measurement application of optical correlation. It is used as a diagnostic for non-stationary objects. This approach is similar to light-beating spectroscopy and laser anemometry. The classical theory of holography presumes a stationary (in a statistical sense) and completely coherent object and reference field. When one tries to register holographically non-stationary processes—such as an assembly of Brownian particles suspended in air or liquid—he or she can record only a snapshot of the assembly. This snapshot remains immovable during the exposure time, and the remaining information is erased due to time averaging.
Holographic associative memory with recording nonlinearity. Reconstruction of Fourier-transform holograms showing autocorrelation of the “object + reference” recording field. The halo around the central point is the autocorrelation image of the object itself.
Opt. Eng. 34, 1079 (1995).
By varying exposure time, one can reconstruct from holographic data the size distribution of particles as well as the particles’ parameters of mobility, such as the velocity distribution function and the rate of sedimentation. These data can be extracted from particle arrangement images that are reconstructed from the set of holograms recorded at various exposure times. The method provides unique time resolution that reaches magnitudes of 10−6 sec.
Holography is important not only for laboratory investigations, but also for solving ecological monitoring and biomedical optics problems.
Characterization of rough surfaces
Scientists have developed highly efficient approaches and portable measuring devices to characterize slightly rough, intermediately rough and very rough surfaces. Accurate surface roughness measurements are critical in many scientific and industrial tasks. New correlation optics techniques are especially practical in astronomy, where the surface control for mirrors and lenses must be carried out with interference accuracy.
Slightly rough surfaces are almost mirror-like. Researchers have created an operational model of a portable device that characterizes such surfaces. It provides highly accurate measurements due to optical channel data processing within an infinitely extended zero interference fringe, and also because of its high sensitivity by modulation collection of data. (See sidebar.)
Surfaces with intermediate roughness cannot be considered slightly rough because they have a regular component of scattered radiation that is not completely destroyed. The regular component of scattered radiation forms a primary source image.
Very rough surfaces occur when the parameters of roughness become so large that the regular component of scattered radiation vanishes. This technique involves the analysis of the longitudinal correlation function reduction of a probe due to increasing dispersion of the partial path delay function. As a result of probing light scattering with limited longitudinal surface coherence and large inhomogeneities, partially scattered wavelets acquire such large delays that the corresponding wave trains are less and less superposed. This results in a decrease of the maximum magnitude of the longitudinal correlation function of the scattered field, and it is accompanied by the elongation of a wave train.
The characteristics of the resulting beam can be reliably determined by using the Michelson’s interferometer arrangement. By calculating the decrease of the maximal magnitude of the longitudinal correlation function and its spreading (for example, at half-width level), one can reconstruct the path delay’s function and, in such a manner, the data from sample properties with large surface inhomogeneities. This technique is also used to analyze femtosecond and picosecond laser pulses, which possess very limited temporal coherence.
Once in a blue moon. Image of the moon (left), and the same moon photographed with colorless glass samples with smaller (central) and larger (right) surface roughness.
Opt. Express 14, 7579 (2006).
The concept of rough surface characterization can be illustrated by viewing the moon through varying grades of ground glass. Under surface illumination by white light, the source image appears intensely colored. Coloring in blue or in red depends on the ratio σ/λ (σ being RMS deviation of surface profile from a mean surface line, and λ is wavelength). As this ratio increases, blue is replaced by red.
Optical correlation characterization provides a simplified method for modeling light-scattering objects and media. The transformation (reduction) of coherence radiation that comes with the interaction of various light-scattering objects follows a general scenario: An element of an object is optically excited; next, the excitation transfers to adjusting elements of the object; finally, the process results in the formation of correlation zones that retransmit at least partially coherently, with concordance in frequency, amplitude, phase and polarization. This approach can now be easily used in physical situations, from nanoparticles to super-resolution near-field microscopy.
A portable device for controlling slightly rough surfaces
Microelectronics, astronomy and other optics-related industries require precise and real-time solutions for surface processing and thin film fabrication on a nanometer scale. Researchers have shown that using a portable shearing interferometer for surface roughness control is often faster and more accurate than the passive laboratory measuring devices that are commonly used.
A shearing interferometer is composed of non-contact sensors. It controls surface roughness by causing the object field to interfere with itself, rather than with the reference field, thus making it possible to measure arbitrarily shaped surfaces with a radius of curvature larger than 0.2 m. This is especially important in the space industry to monitor the quality of mirrors made by diamond microsharpening, and in the photochemical industry to monitor the quality of calendar shafts.
The operational model pictured here is mounted directly on the polishing machine tool. It can be used to control the surface quality during manufacturing. Researchers have observed sensitivity estimated by the root-mean-square wave (RMS) height parameter down to 0.001 m while using the device.
Portable shearing interferometers could provide surface roughness control with various reflection coefficient magnitudes and multiplication factor control, ensuring the proper diagnostics of large surface roughness.
RMS range: 0.002 to 0.06 μm
Accuracy: 0.001 μm
Indication rate: One measurement/second
Power supply: 6 V
Size: 150 mm × 50 mm × 20 mm
Therefore, scientists have paid great attention to the study of coherent characteristics of near-field scattering light. They have been motivated in part by the unique imaging properties of evanescent waves that provide enhanced resolution, which can be as fine as 10 nm through the exploitation of visible or infrared radiation. These investigations have led to the use of tiny light-scattering particles—for example, gold—as receiving-transmitting optical antennas. Similar to radiowave and microwave antennas, optical antennas convert free propagating radiation energy to localized energy, and vice versa. They exploit the unique properties of metal nanostructures, which behave as strongly coupled plasmas at optical frequencies.
While radio antennas were developed for communication, optical antennas were primarily invented for microscopy; an optical antenna replaces the traditional focusing lens or objective, concentrating external laser radiation to dimensions smaller than the diffraction limit. The distance between molecule and optical antenna is important. There is no interaction between molecule and antenna if the distance is too far, and if the distance is too short, all the energy is dissipated into heat.
Optical correlation techniques are now advanced enough to enable singular optics applications of incompletely coherent light fields. Singular optics deals with peculiar wave structures referred to as amplitude zeroes, wave front dislocations or optical vortices. Scientific interest in these wave structures has inspired the development of singular-optical micro- and nanomanipulators and molecular motors.
Research in this area initially concerned completely spatially coherent, monochromatic light fields—such as Laguerre-Gaussian modes or homogeneously polarized (scalar) speckle fields. However, experts in singular optics rightly predicted that interest would eventually focus on more general cases, such as when light fields bearing singularities are not completely spatially coherent, homogeneously polarized or monochromatic.
Optical correlation techniques—for example, interference, diffraction, polarimetrology and holography—are the most effective singular optics tools for the detection and diagnosis of phase singularities in scalar and in vector optical fields, and also for the creation of vortex beams with controlled parameters.
White-light speckles with forklets. Singularity obtained in a white light beam passing a double-axial crystal placed between matched polarizer and analyzer with a reference wave.
Opt. Express 13, 8179 (2005).
2-D maps of intensity distributions
Polarization-interference metrology of light field coherence can transition from theory to actual experimental tools because of the charge-coupled device cameras for rapid and reliable 2-D maps of various parameters of a field. Several interconnected approaches have been put forward to describe far and near inhomogeneously polarized fields, as well as such fields at the image plane.
Probably the most interesting application of correlation optics is its use in registering 2-D maps of intensity distributions. At first glance, it would seem that registering such maps with the polarization parameter computation would give us comprehensive information about a field’s structure. However, this is not completely true. Fields characterized by the same statistics can be differentiated in the way these statistics are collected. To implement this differentiation, researchers must not be confined to collecting second-order statistics. They must also find higher-order statistics, such as the kurtosis coefficient and eccentricity, by computing them from experimental data. In doing so, they can differentiate fields—for example, globally unpolarized fields made by different sets of polarization states.
This approach has been successfully applied in biomedicine. Here, it is used to characterize the physiological state of biological tissues, aiding in disease diagnosis. It has also allowed researchers to develop the technique of coherent polarization tomography of biological tissues, which provides noninvasive diagnostic capability.
Advancements made possible by correlation optics
Correlation optics applications and techniques have brought about several discoveries that have advanced the field of optics and photonics. For example:
The common complex amplitude of completely coherent monochromatic fields can support phase singularities and also support any complex parameter of the field. The specific set of singularities is intrinsic to each level of description.
An autocorrelation technique based on the Young-Rubinowicz model of diffraction can be used for the detection and diagnosis of phase singularities of the spatial correlation functions and complex degrees of coherence of partially coherent fields. This technique has been expanded for use on polychromatic (white light) beams for the detection of spectral component phase singularities.
There are vector singularities that are inherent in partially coherent, inhomogeneously polarized combined beams—including the complex degree of polarization.
Researchers can elaborate on the Poynting vector singularities at light fields with amplitude zeroes.
Leaders in the field have predicted and observed spectral modifications of white light in the vicinity of amplitude zeroes of spectral components. The chromascopic technique has been introduced for determining the peculiarities of universal color distribution near “dark light.”
Many researchers have investigated optical field polarization. Important work in this area includes: 1) introducing two-point Stokes parameters and interpretation of their properties; 2) applying the Stokes parameters’ observed contrast into the Young’s interference arrangement for metrology of coherence; 3) developing Stokes-holography for recording and reconstructing objects using polarization fringes; 4) developing optical vortex metrology; and 5) measuring displacement and flow with phase singularities.
Since 1993, 10 biannual international conferences on correlation optics have been held at Chernivtsi University in Ukraine. Predicting future trends is always one of the topics of discussion.
The use of correlation optics will lead to new applications of nondestructive characterization (diagnostics) of optical fields as well as the objects whose structure causes the fields to form with specific characteristics.
This emerging field has provided efficient measuring techniques as well as methods for controlling and manipulating very fine quantities of matter at the scales typical for micro- and nanophotonics. The development of these applications may prove to be important for product quality control in the optical, electronic and machine-building industry; in solid state physics (control of thin films and crystal growth); in precise chemistry and biology; as well as in biomedical optics and ecological monitoring. What’s next?
Oleg V. Angelsky, Peter V. Polyanskii and Christina V. Felde are with the department of correlation optics, Chernivtsi National University, Ukraine. Angelsky is an OSA and SPIE Fellow.
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