In this paper, an approach for beam collimation by pupil segmentation is proposed. In this approach, the divergent or convergent wavefront of the beam to be collimated is divided into a series of subwavefronts by a microlens array, and the beam collimation is realized by comparing the difference of centroids between the actual spots and the reference ones under the paraxial approximation. In the experiment, the size of the beam to be collimated is limited by a stop aperture to satisfy the paraxial approximation. Using the proposed method, a divergent beam is collimated by a doublet with a focal length of 100 mm under the paraxial approximation. The test results of the collimated beam by a Shack-Hartmann sensor show that the root mean square of the wavefront of the collimated beam is 0.02 λ, having a good agreement with results of the proposed method. The experimental results show that the method is simple, low cost and highly accurate.
Wavefront sensing from an extended object is a challenging task since the phase to be sensed is disturbed by the one generated from the structure of the extended object. To address this problem, a general wavefront sensor is proposed. The configuration of the proposed sensor consists of a field lens, a collimating lens, a lenslet array, and a camera. The field lens, the first element of this sensor, ensures that each lenslet collects the same information of the extended object, which is a basis for the reconstruction of the distorted wavefront from the extended object using the proposed sensor. The fundamental strategy of the sensor is converting the scenario of wavefront sensing from an extended object into the traditional one from a point source by eliminating the Fourier spatial spectrum of the extended object in the frequency domain. As a result, the distorted wavefront can be reconstructed using the algorithm of the Shack–Hartmann wavefront sensor. Numerical simulations and experiments both verify the feasibility and accuracy of the proposed sensor for direct wavefront sensing from any types of extended objects.
An approach for wavefront reconstruction based on a defocused Shark–Hartmann sensor is proposed. In this approach, not only the first-order origin moment (local slope of the input wavefront) but also the second-order central moment (local curvature of the input wavefront) of each spot in the intensity pattern is used to reconstruct the input wavefront. By introducing the second-order moment, an improvement of reconstruction accuracy can be obtained. As the ambiguity of the sense of the local curvature of the input wavefront exists in the scheme of the conventional Shack–Hartmann sensor in focus, a defocusing scheme is adopted to solve this problem. Based on modal and zonal methods, respectively, the corresponding algorithms are invoked to reconstruct the wavefront from the map consisted of both local slopes and curvatures. Numerical experiments show that the reconstructed wavefront by the proposed method is more accurate, in comparison to the result by the conventional method. It should be mentioned that the defocused sensor used in the proposed method sacrifices, to some extent, the dynamic range of measurement.
This book explains how to understand and analyze the working principles of optical systems by means of optical theories and case studies. Part I focuses mainly on the theory of classical optics, providing an introduction to geometrical and wave optics, and some concepts of quantum and statistical optics. Part II presents case studies of three practical optical systems that comprise important and commonly used optical elements: confocal microscopes, online co-phasing optical systems for segmented mirrors, and adaptive optics systems. With the theoretical background gained in Part I, readers can apply their understanding of the optical systems presented in Part II to the conception of their own novel optical systems. The book can be used as a text or reference guide for students majoring in optics or physics. It can also be used as a reference for any scientist, engineer, or researcher whose work involves optical systems.
Quadrant photodetector is one of the most popular detection devices for tip/tilt sensing. The measurement range and detection sensitivity, depending on the size of light spot incident on the quadrant photodetector, are theoretically analyzed and discussed in the application cases of the uniform irradiance distribution and of Gaussian irradiance distribution of the incident light spot. According to the theoretical results, the larger the size of the light spot is, the greater the measurement range of the quadrant photodetector, and the smaller the detection sensitivity of the quadrant photodetector.
An approach for the online co-phasing of segmented telescopes using dual wavelength digital holography has been
proposed. In this approach, two digital interferograms, one fringe pattern for one wavelength, which are acquired by a
high speed CCD camera using a Mach-Zehnder point diffraction interferometer, are required. By these two fringes for
two different wavelengths, the phase of a synthetic wavelength for the segmented telescope can be extracted using the
digital holography technique. To overcome errors caused by atmosphere and measurement noises, the piston and tip/tilt
coefficients for each segment of the telescope are acquired by fitting the plane from the phase of the synthetic
wavelength in each segment of the telescope. The performance of the method is tested by co-phasing of a simulated
telescope with 37 hexagonal segments with the existence of turbulence and noise. The numerical experimental results
show that co-phasing of the segmented telescope with high accuracy can be achieved by dual wavelength digital
holography.
A modal control optimization method for adaptive optics on the tempo-spatial domain is presented. The spatial modes of
the adaptive optics system can be obtained by the singular value decomposition of the response function matrix of the
adaptive optics system. The number of correction modes is determined dynamically by the root mean square estimation
of the residual aberration after the correction with different number of modes. A Smith compensator is designed to
reduce the time delay effect on the closed-loop system. The modal optimization method is experimentally verified by
compensating phase distortion produced by artificial atmospheric turbulence in laboratory. Experimental results show
that the correction capability of the adaptive optics system can be greatly improved in comparison to that of the generic
modal gain integrator approach with the fixed number of correction modes. The modal control optimization method is an
attractive and practical alternative to adaptive optics control.
The stochastic parallel gradient descent algorithm based on the generalized phase diversity wavefront sensor is presented
for co-phasing of segmented mirrors. Cost functions of the optimization algorithm were built up in different circular
zones for intensity images of the sensor. In order to achieve high accuracy for co-phasing, four phase diversity functions
with increasing amplitudes were applied to the sensor for improving the strength of output signal from the wavefront
sensor during the aberrations of the segmented mirror decreasing with the co-phasing process. A simulated segmented
mirror was used to test the feasibility of this method. The numerical experiments show that the co-phasing accuracy is
very high for the aberrations of the segmented mirrors less than 1.5 wavelengths. And the algorithm is very robust and
noise tolerant.
A nonlinear image technique for characterization of the optical nonlinearities is used to investigate the solid
semiconductor ZnSe at 600 nm. The method based on a 4f nonlinear image technique with a phase object is used to
obtain the diffraction pattern of the nonlinear filter in solid ZnSe located at the Fourier plane by a CCD camera. The
nonlinear absorption coefficient and nonlinear refraction index were both obtained by fitting the nonlinear image. Good
agreement between the experiment data and the simulated result are obtained indicating a sensitive and powerful method
for nonlinear optical measurements.
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