Sijiong Zhang

Generalized phase diversity for wave-front sensing.

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.

Three-dimensional particle imaging by wavefront sensing

We present two methods for three-dimensional particle metrology from a single two-dimensional view. The techniques are based on wavefront sensing where the three-dimensional location of a particle is encoded into a single image plane. The first technique is based on multiplanar imaging, and the second produces three-dimensional location information via anamorphic distortion of the recorded images. Preliminary results show that an uncertainty of 8 microm in depth can be obtained for low-particle density over a thin plane, and an uncertainty of 30 microm for higher particle density over a 10 mm deep volume.

Phase retrieval using a modified Shack–Hartmann wavefront sensor with defocus

This paper proposes a modified Shack-Hartmann wavefront sensor for phase retrieval. The sensor is revamped by placing a detector at a defocused plane before the focal plane of the lenslet array of the Shack-Hartmann sensor. The algorithm for phase retrieval is an optimization with initial Zernike coefficients calculated by the conventional phase reconstruction of the Shack-Hartmann sensor. Numerical simulations show that the proposed sensor permits sensitive, accurate phase retrieval. Furthermore, experiments tested the feasibility of phase retrieval using the proposed sensor. The surface irregularity for a flat mirror was measured by the proposed method and a Veeco interferometer, respectively. The irregularity for the mirror measured by the proposed method is in very good agreement with that measured using the Veeco interferometer.

Co-phasing of the segmented mirror based on the generalized phase diversity wavefront sensor

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.

Theoretical analyses for the relationship between the performance of quadrant photodetector and the size of incident light spot

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.

Ground layer adaptive optics system simulation for the 2.5m telescope in Dome A

The Antarctic is an ideal place for optical and infrared astronomy observations. Chinese scientists are planning to build a 2.5m telescope in Dome A. The telescope will be built in a tower about 15 meters high to avoid the ground layer atmospheric turbulence. The Ground layer Adaptive Optics system (GLAO) will also be suggested to be installed to further reduce the seeing. The GLAO system with one laser guide star, one deformable mirror and one wide field Shack-Hartmann wavefront sensor is designed and simulated. The Strehl ratio has increased 2 to 3 times in visible and infrared band in 20 arc min field of view.

Small angle expansion: a solution to the phase-retrieval problem using generalized phase diversity in pupil space

Phase diversity is a phase-retrieval algorithm that uses a pair of defocused intensity images taken symmetrically about the wavefront to be determined. Generalised phase diversity is a phase-retrieval algorithm that uses diversity functions other than defocus. The approach adopted assumes that unknown phase changes satisfy the small-angle approximation over spatial regions that can be selected by choice of the diversity function. For smooth functions, and for discontinuous functions with only small discontinuities, this leads to a very simple analytic solution. Computer simulations were used to validate this method for the retrieved phase.

Adaptive Aperture Synthesis

High-resolution imaging can be achieved by optical aperture synthesis (OAS). Such an imaging process is subject to aberrations introduced by instrumental defects and/or turbulent media. Redundant spacings calibration (RSC) is a snapshot calibration technique that can be used to calibrate OAS arrays without use of assumptions about the object being imaged. Here we investigate the analogies between RSC and adaptive optics in passive imaging applications.

Extended wavefront sensing with novel diversity functions

Generalized Phase Diversity (GPD) is a phase retrieval algorithm which requires a pair of intensity images. These are created by applying equal and opposite diversity phase to the input wavefront. Unlike traditional phase diversity methods GPD is not limited to the use of defocus as the applied diversity phase. The conditions that a suitable diversity function must satisfy for use in a null sensor were presented at the 4th IWAOIM. Following our recent development of a small angle solution to the inverse problem, in this paper the GPD method will be extended to use as a full wavefront sensor. This method has a wide range of applications, including laser beam shaping, analysis of segmented optics, and metrology. Results will be presented to show the versatility and accuracy of this novel wavefront sensing method.

Case Study 1: Confocal Microscopes

The confocal microscope is an optical instrument that can obtain a highresolution 3D image of the microscopic structures of an object. In this chapter, the confocal microscope is examined—from its working principle to its optical layout—using mainly geometrical optics. With this example, and using knowledge of geometrical optics, readers can acquire some skills to understand the working principles of other optical systems. In the following sections, first, the fundamentals of a standard optical microscope are summarized in order to help readers understand the confocal microscope; next, the basic principles of the confocal microscope and some of its main components are provided; finally, two typical confocal microscopes are presented.