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This thesis mainly concerns a continuous-time behavioral consumption model under Kahneman and Tversky’s cumulative prospect theory. Mathematically this is a non- concave maximization problem because of the presence of an S-shaped functional and the presence of so-called probability distortions. By using a quantile method and divide-and-conquer scheme, we solve the problem quite explicitly and the optimal consumption is in general characterized in two parts: the agent has rich consumption above the benchmark in good situations and suffers from hunger (i.e. no consumption) in bad situations. An example is given to show that judging whether the market is good or bad depends highly on the agent’s benchmark. Finally we give the strategy for optimal consumption and portfolio selection to maximize behavioral utilities from both consumption and terminal wealth.

A general resonant frequency locking scheme for a field-widened Michelson interferometer (FWMI), which is intended as a spectral discriminator in a high-spectral-resolution lidar, is proposed based on optimal multi-harmonics heterodyning. By transferring the energy of a reference laser to multi-harmonics of different orders generated by optimal electro-optic phase modulation, the heterodyne signal of these multi-harmonics through the FWMI can reveal the resonant frequency drift of the interferometer very sensitively within a large frequency range. This approach can overcome the locking difficulty induced by the low finesse of the FWMI, thus contributing to excellent locking accuracy and lock acquisition range without any constraint on the interferometer itself. The theoretical and experimental results are presented to verify the performance of this scheme.

In this paper, a new panoramic annular lens (PAL) with a super wide angle of (30°-120°)×360° is introduced that consists of two parts: a panoramic front unit (PFU) and a relay lens. First, two PFU arrangements referring to the block structured panoramic front unit (BSPFU) and the shell structured panoramic front unit are compared and analyzed in terms of their field curvature correction ability and structural feasibility for obtaining a wide angle PAL. From the comparison, the BSPFU arrangement turns out to be more promising for its good field curvature correction, structure compactness, and convenience for manufacture and assembly. Second, a relay lens composed of six lenses with three Qsubbfs/subaspheres has been designed to match the BSPFU. Finally, image performance analysis of the optimized super wide angle PAL is presented. The results show that the designed PAL equipped with a BSPFU and a Qsubbfs/subaspherized relay lens achieves good performance under a super wide field of view of (30°-120°)×360°.

A field-widened Michelson interferometer (FWMI), which is intended as the spectroscopic discriminator in ground-based high-spectral-resolution lidar (HSRL) for atmospheric aerosol detection, is described in this paper. The structure, specifications and design of the developed prototype FWMI are introduced, and an experimental approach is proposed to optimize the FWMI assembly and evaluate its comprehensive characteristic simultaneously. Experimental results show that, after optimization process, the peak-to-valley (PV) value and root-mean-square (RMS) value of measured OPD variation for the FWMI are 0.04λ and 0.008λ respectively among the half divergent angle range of 1.5 degree. Through an active locking technique, the frequency of the FWMI can be locked to the laser transmitter with accuracy of 27 MHz for more than one hour. The practical spectral discrimination ratio (SDR) for the developed FWMI is evaluated to be larger than 86 if the divergent angle of incident beam is smaller than 0.5 degree. All these results demonstrate the great potential of the developed FWMI as the spectroscopic discriminator for HSRLs, as well as the feasibility of the proposed design and optimization process. This paper is expected to provide a good entrance for the lidar community in future HSRL developments using the FWMI technique.

A new method for long focal-length measurements is proposed. In this method, we employ divergent beam and two Ronchi gratings of different periods, as the alternative to collimated beams and two identical gratings in traditional method, to realize achieve higher accuracy. Moreover, with divergent beam, the full-aperture measurement is easily realized when detect large diameter lens. The experiments demonstrated the proposed method features high accuracy and repeatability.

In the flat sub-aperture stitching test, the dominant e error comes from two dimensional translation stage that carries the flat under test, which contains tilt and position error i.e., the alignment error. In order to analyze the influence of alignment error on stitching precision, we use Zemax optical software to simulate a system to detect the phase of each sub-aperture of measured flat and add tilt and position errors and random noise to sub-apertures. The simulation model was utilized in this paper to evaluate the mechanical precision of the translation stage in order to meet a required stitching precision of 1/1000λ.

By analyzing the spectral domain’s phase information, the spectrally resolved white-light interferometry (SRWLI) is capable of obtaining the profile with a single frame of interferogram. However, only one-dimensional (1-D) surfaces can be tested with this technique, otherwise the interference patterns under adjacent wavelengths would overlap each other, which would make the whole interferogram hard to identify. We present here a 2-D SRWLI method which can be applied to measure narrow rectangle areas. Frequency comb is produced by means of using a F-P etalon to filter the broadband source. With the filtered frequency comb illumination, the interference patterns under adjacent wavelengths would be separated by a little distance, which enables us to obtain a 2-D profile with a small width. The experimental details of measurement of a step sample are discussed in this paper.

To achieve highly efficient and flexible spectrum sharing in cognitive radio networks, we proposed a queuing method in combined channel aggregation and fragmentation (CAF) strategy for dynamic spectrum access (DSA). We derived the balance equation and evaluated various system performance metrics including blocking probability, dropping probability, spectrum utilization, throughput and mean queuing time by a continuous time Markov chain (CTMC) model. Numerical results show that this CAF with queuing strategy greatly lowers the dropping probability without obviously impacting the blocking probability, and slightly increases the spectrum utilization and throughput of the secondary network compared with the non-queuing case. Moreover, by tuning the bandwidth requirement of each secondary user, different system performance can be achieved.

By analyzing the spectral domain's phase information, one can use spectrally resolved white-light interferometry (SRWLI) to obtain the profile with a single frame of an interferogram. We present here a two-dimensional (2D) SRWLI method that can be applied to measure narrow rectangle areas. A frequency comb is produced by using a Fabry-Perot (F-P) etalon to filter the broadband source. With the filtered frequency comb illumination, the interference patterns under adjacent wavelengths would be separated by a little distance, which enables us to obtain a 2D profile with a small width. The experimental details of measurement on a step sample are discussed in this paper.

Traditional interferometric profilemeter suffers from phase ambiguity problem and sensitivity to environmental disturbance, thus preventing their applications for on-line surface inspections. We propose a new method to obtain the object surface's two-dimensional profile in a single shot using a dispersive interferometer. An air-spaced Fabry-Perot etalon was applied in order to decompose the light from the broadband source into discrete monochromatic constituents with equal wavelength interval. A blazed grating is implemented to effectively separate the interferograms of difference wavelength. As a result, the interference patterns of different wavelengths distributed separately on the CCD camera. By analyzing these patterns one can get the configuration of the original surface. A one-dimensional profiling experiment is carried out to test a surface with steps and the mean error of the result is below 0.2μm.

White-light interferometry is always an extremely useful and powerful tool for optical surface measurement. In this paper, a novelty method based on rapid positioning and fast surface measurement is proposed. The adjustment of optical path difference (OPD) is done automatically by a wavelength scanning method, and the processing of white-light interference patterns is accelerated by GPGPU which stands for General-Purpose computation on Graphics Processing Units, also known as GPU Computing. Graphics Processing Units are high-performance many-core processors in which the data are processed in parallel. As a result, the time we need to obtain a surface shape is reduced to ten percents compared with the conventional white-light interferometry. With these advantages, it is possible to measure a rough and areal surface in a short time.

We introduce a new optical interferometry system for fast areal surface measurement of microscale\ud and nanoscale surfaces that are immune to environmental noise. Wavelength scanning interferometry\ud together with an acousto-optic tunable filtering technique is used to measure surfaces with large\ud step heights. An active servo control system serves as a phase-compensating mechanism to eliminate\ud the effects of environmental noise. The system can be used for online or in-process measurement on\ud a shop floor. Measurement results from two step height standard samples and a structured surface\ud of a semiconductor daughterboard are presented. In comparison with standard step height specimens,\ud the system achieved nanometer measurement accuracy. The measurement results of the semiconductor daughterboard, under mechanical disturbance, showed that the system can withstand environmental\ud noise.

Absolute interferometric testing of spherical surfaces is one of effective methods for ultra-precision testing, which can eliminate the systematic errors. In this paper, we discuss the absolute measurement of spherical surfaces and analyze the influence of errors existed in the organism comprehensively. To improve the testing precision, it is necessary to remove the alignment errors such as tilt and defocus. The traditional methods remove alignment errors by low-level approximation, so they may be not effective for the small F-number surface. To solve this problem, we propose a novel measurement with high-order approximation model. The simulation and experiment results show that: while the error between high-order approximation model and low-level approximate model is small on tilt, it is large on defocus, and the error will become larger when the F-number of testing surface becomes smaller; alignment errors can be well adjusted by our high-order approximation model.

In this paper, a novel direct writing technique using submicron-diameter fibers is presented. The submicron-diameter fiber probe serves as a tightly confined point source and it adopts micro touch mode in the process of writing. The energy distribution of direct writing model is analyzed by Three-Dimension Finite-Difference Time-Domain method. Experiments demonstrate that submicron-diameter fiber direct writing has some advantages: simple process, 350-nm-resolution (lower than 442-nm-wavelength), large writing area, and controllable width of lines. In addition, by altering writing direction of lines, complex submicron patterns can be fabricated.

Light beam scanning using a dispersive element and wavelength tuning is coupled with fiber-optic interferometry to realize a new surface measurement instrument. The instrument is capable of measuring nanoscale surface structures and form deviations. It features active vibration compensation and a small optical probe size that may be placed remotely from the main apparatus. Active vibration compensation is provided by the multiplexing of two interferometers with near common paths. Closed loop control of a mirror mounted on a piezoelectric transducer is used to keep the path length stable. Experiments were carried out to deduce the effectiveness of the vibration compensation and the ability to carry out a real measurement in the face of large environmental disturbance.

This paper discusses the pulse signal of a highly sensitive lateral deformable optical microelectromechanical systems (MEMS) displacement sensor based on Wood's anomalies and its corresponding tolerance. The optical reflection amplitude of the device changes with the displacement of the nanostructured grating elements. Unexpectedly, the device's original sinusoidal signal develops into a new signal form (i.e., a pulse signal), when the air gap between the two layers of gratings decreases. Since the slope of the pulse signal, namely 2.5%/nm (i.e., 0.65 dB/nm), is eight times higher than that of the original signal form, namely 0.3%/nm (i.e., 0.03 dB/nm), the sensitivity of the structure improves by eight times. However, this device is very sensitive to parameters such as its wavelength, period, duty ratio, and air gap. In this paper we used rigorous coupled wavelength analysis (RCWA) to analyze and optimize the respective influence of each parameter on the device's performance. We have introduced two methods to search for the optimal setting and have demonstrated the optimal settings of different incident lights. The simulation results indicate that it is close to 85% possible to achieve an actual device with the highest slope superior to 0.5%/nm and it is 64% possible that the highest slope of an actual device falls in the interval ranging from 1.0%/nm to 2.0%/nm. All the simulated data helped us better understand the tolerance of the pulse signal and guide us toward the development of an actual device.

A pattern recognition model for aerosol classification with atmospheric backscatter lidars is proposed and studied in detail. The theoretical framework and the implementation process of the proposed model are presented. Computer simulations have been carried out to verify the practicability and robustness of this model. The k-fold cross-validation method is employed in the process of classifier designing to choose the proper decision rule, which is mainly based on statistical pattern recognition theory. At the same time, the validity of the model is evaluated. The generalized self-validation is also carried out in the computer simulations to verify the stability of the model. The analysis of the performances in reduced status, especially the instance of application to Cloud-Aerosol Lidar with Orthogonal Polarization, demonstrates the generalization ability and performance of this model.

A subnanometer resolution displacement sensor based on a grating interferometric cavity with intensity compensation and phase modulation is proposed and experimentally demonstrated in this paper. The grating interferometric cavity is composed of a frequency-stabilized laser source, a diffraction grating, and a mirror. To realize a subnanometer resolution, the intensity compensation and phase modulation technique are introduced, which are achieved by an intensity compensation light path, three closed placed photodetectors, a processing circuit and a piezoelectric ceramic transducer, and a lock-in amplifier. The intensity compensation technique can improve the stability of the output intensity signal greatly while the phase modulation technique can increase the signal-to-noise ratio dramatically. The detected signal is intensity modulated and processed by a particular arithmetic circuit. Experimental results indicate that the sensitivity of this displacement sensor is 44.75 mV/nm and the highest resolution can reach 0.017 nm, which is 27 times better than the one without intensity compensation and phase modulation. As a high-performance sensor with immunity to electromagnetic interference, this displacement sensor has potential to be used in nanoscience and technology.

We introduce a new surface measurement method for potential online application. Compared with our previous research, the new design is a significant improvement. It also features high stability because it uses a near common-path configuration. The method should be of great benefit to advanced manufacturing, especially for quality and process control in ultraprecision manufacturing and on the production line. Proof-of-concept experiments have been successfully conducted by measuring the system repeatability and the displacements of a mirror surface.

A new accurate method for long focal-length measurement based on Talbot interferometry is proposed. A divergent beam and two Ronchi gratings of different periods are employed, as the alternative of the collimated beam and two identical gratings, to achieve higher measurement accuracy. Moreover, with divergent beam, lenses of large aperture can be easily measured without scanning, which is required when it comes to traditional collimated beam. Numerical analysis and experiments were carried out. The results demonstrate the proposed method features remarkably high accuracy and repeatability.

A common-path and compact wavefront diagnosis system for both continuous and transient wavefronts measurement is proposed based on cross grating lateral shearing interferometer (CGLSI). Derived from the basic CGLSI configuration, this system employs an aplanatic lens to convert the wavefront under test into a convergent beam, which makes it possible for CGLSI to test the wavefront of collimated beams. A geometrical optics model for grating pitch determination and a Fresnel diffraction model for order selection mask design are presented. Then a detailed analysis about the influence of the grating pitch, the distance from the cross grating to the order selection mask and the numerical aperture of the aplanatic lens on the system error is made, and a calibration method is proposed to eliminate the system error. In addition, the differential Zernike polynomials fitting method is introduced for wavefront retrieval. Before our experiment, we have designed several grating pitches and their corresponding order selection mask parameters. In the final comparative experiment with ZYGO interferometer, the wavefront diagnosis system exhibits both high precision and repeatability.

In this paper, we report the recent progress in optical-beam scanning fiber interferometry for potential online nanoscale surface measurement based on the previous research. It attempts to generate a robust and miniature measurement device for future development into a multiprobe array measurement system. In this research, both fiber-optic-interferometry and the wavelength-division-multiplexing techniques have been used, so that the optical probe and the optical interferometer are well spaced and fast surface scanning can be carried out, allowing flexibility for online measurement. In addition, this system provides a self-reference signal to stabilize the optical detection with high common-mode noise suppression by adopting an active phase tracking and stabilization technique. Low-frequency noise was significantly reduced compared with unstabilized result. The measurement of a sample surface shows an attained repeatability of 3.3 nm.

A heterodyne Fourier transform spectroscopy is proposed in which a double-grating frequency shifter was used to provide the stable achromatic frequency shift. Compared with conventional Fourier transform spectroscopy, our method can obtain spectra with high sensitivity due to optical frequency modulation and high wavelength resolution due to there being no limit for its scanning range. A wavelength resolution of 0.16nm was achieved in the spectra measurements.