Wenzi Zhang

Point spread function characteristics analysis of the wavefront coding system

Most of the previous imaging characteristics analysis of the wavefront coding system has been carried out within the frequency domain. In this paper, the stationary phase method is employed to perform the analysis within the spatial domain. The approximate expression of point spread function (PSF) in the presence of defocus aberration is derived for the system with a cubic phase mask, which shows a good agreement with the Fast Fourier Transform (FFT) approach. Based on this, the PSF characteristics are analyzed in terms of the boundaries, oscillations and sensitivities to defocus, astigmatism and coma.

Free-form reflector optimization for general lighting

A slope angle-based reflector profile optimization method is introduced at the first time. Compared to the traditional profile-based optimization method, better optimization results are obtained with this method. Design examples of reflectors for general lighting applications are given to compare both types of optimization methods. Disadvantages, such as range definition, range overlapping, and parameter-dependent problems, which existed in the traditional profile-based optimization method can be totally overcome with the proposed method.

Wide viewing angle skewed effect of the point spread function in a wavefront coding system

The point spread function (PSF) of a wavefront coding (WFC) system with a cubic phase mask is analyzed with a wide viewing angle based on physical optics for what is believed to be the first time. Two coordinate transformations are made to generate a pupil function, from which we obtain the encoded PSF of the WFC system with defocus parameters W(020) and object angles alpha and beta. The encoded PSFs are further side extended as the object angles get wider. When alphabeta<0, the included angle ? of encoded PSF will skew to an obtuse angle. When alphabeta=0, ? remains orthogonal; when alphabeta>0, ? will skew to an acute angle. Furthermore, the effect of skew and side extension is even symmetric about W(020). As a result, the wide viewing angle has a bad effect on the imaging quality of the WFC system.

Ray aberrations analysis for phase plates illuminated by off-axis collimated beams

Approximate expressions of the ray aberrations for off-axis collimated beams and free form phase plates with a small derivative magnitude are derived with the defocus aberration taken into account. The cubic phase plate, which is one of the most commonly used phase plates in wavefront coding imaging systems, is illustrated as an example. The approximate expressions for the upper and lower boundaries of ray map, and the spot size in the vicinity of the focal plane are derived. The sensitivity to the defocus aberration and the variation of the induced aberrations with respect to the field positions are analyzed with derived approximate expressions as well. Some characteristics unmentioned before are derived, showing a good agreement with the exact aberrations. Finally some useful guidelines are given for the design of imaging systems with phase plates.

Compact LED based LCOS optical engine for mobile projection

With the development of high power LED (light emitting diode) technology and color filter LCOS (liquid crystal on silicon) technology, the research on LED based micro optical engine for mobile projection has been a hot topic recently. In this paper one compact LED powered LCOS optical engine design is presented, which is intended to be embedded in cell phone, digital camera, and so on. Compared to DLP (digital light processor) and traditional color sequential LCOS technology, the color filter based LCOS panel is chosen for the compact optical engine, this is because only white LED is needed. To further decrease the size of the optical engine, only one specifically designed plastic free form lens is applied in the illumination part of the optical engine. This free form lens is designed so that it plays the roles of both condenser and integrator, by which the output light of LED is condensed and redistributed, and light illumination of high efficiency, high uniformity and small incident angle on LCOS is acquired. Besides PBS (polarization beam splitter), LCOS, and projection lens, the compact optical engine contains only this piece of free form plastic lens, which can be produced by plastic injection molding. Finally a white LED powered LCOS optical engine with a compact size of less than 6.6 cc can be acquired. With the ray tracing simulation result, the light efficiency analysis shows that the output flux is over 8.5 ANSI lumens and the ANSI uniformity of over 80%.

Image restoration based on generalized minimal residual methods with antireflective boundary conditions in a wavefront coding system

The point spread function (PSF) is asymmetric in a wavefront coding (WFC) system with cubic phase mask (CPM). The image formation of the WFC system is described as the generalized Sylvester matrix equation. With Tikhonov regularization, a global generalized minimal residual method (Gl-GMRES) algorithm is used to obtain the restored sharp image. For this large-scale, linear, and discrete, ill-posed problem, we introduce a Kronecker product approximation of the blurring operator to reduce the computation consumption. To eliminate ringing effect, four boundary conditions (BCs) are considered in the image restoration: periodic BCs, zero BCs, reflective BCs, and antireflective BCs. Analysis and numerical results show that the antireflective BCs provide better results than others. The experiment results show that the Gl-GMRES algorithm with antireflective BCs is more effective than the classic Wiener filter.

Pupil design based on Fisher information optimization to extend field depth in practical optical system

Wavefront coding (WFC) is used to extend the field depth of an incoherent optical system by employing a phase mask on the pupil. We uses a Fisher information (FI) metric based optimization method to design a phase mask by taking the modulation transfer function (MTF) of the practical optical system into consideration. This method can modulate the wavefront so that the point spread function and optical transfer function are insensitive to the object distance. The simulation results show that the optimized phase mask based on the proposed method can further improve the defocusing image quality while maintaining the focusing image quality.

A new polarization multiplexing method for the micro LCOS projector optical system

In this paper we present a new polarization multiplexing method for the micro LCOS projector optical system. We use calcite to separate the P and S light with respect to the PBS used in the traditional way. The specific method is described as follow: the special lens group or TIR is used to collimate emission ray from the light source. The ray from the lens is changed into approximate parallel light. A convergent component is used to get the convergence light on the exit facet of the calcite. Because of the structure characteristic of the calcite, the angel between optical axis of crystal and cleavage surface is 45 degree. Then we can get two separate convergence light spot on the exit facet of the calcite which stands for the P and S light respectively. The linear half wave plate is used to convert the state of the polarization. Then light pipe and relay imaging lens are used to meet the requirements of the uniformity and incident angle on the micro LCOS chip.

Design of Objective Lenses to Extend the Depth of Field based on Wavefront Coding

Wavefront coding extended the depth of field to a great extent with simpler structure compared to confocal microscope. With cubic phase mask (CPM) employed in the STOP of the objective lens, blurred images will be obtained in charge coupled device (CCD), which will be restored to sharp images by Wiener filter. We proposed that one CPM is used in one microscope although there are different objective lenses with different power indices. The microscope proposed here is the wavefront coding one when the CPM is used in the STOP; while it is the traditional one when a plane plate is used in the STOP. Firstly, make the STOP in the last surface of the lens, and then add a plane plate at the STOP with the same material and the same center thickness of the CPM. Traditional objective lenses are designed, based on which wavefront coding system will be designed with the plane plate replaced by a CPM. Secondly, the parameters of CPMs in different objective lenses are optimized to certain ranges based on metric function of stability of modulation transfer function (MTF). The optimal parameter is chosen from these ranges. A set of objective lenses is designed as an example with one CPM. The simulation results shows that the depth of field of 4X, 10X, 40X, 60X and 100X objective lenses with the same CPM can reach to 400um, 40um, 24um, 16um and 2um respectively, which is much larger than 55.5um, 8.5um, 1um, 0.4um and 0.19um of the traditional ones.

Fly-eyes illumination analysis

The Fly-eyes element has been widely applied to acquire uniform illumination in microscope, printing, projection, and so on. With large number of fly-eyes pieces and specified aperture shape, illumination of high efficiency, high uniformity, and specified area shape can be acquired. In this paper, mathematical expressions for fly-eyes illumination are derived for free form incoming light distribution. With these expressions, the reason why uniform illumination can be acquired with fly-eyes is given, and the defects of fly-eyes illumination is also discovered. According to traditional design experience, the illumination uniformity acquired by fly-eyes illumination will be increased with the increment of fly-eyes number. But with the derived expressions, it can be found that there are some limitations for this experience. For some odd symmetrical illumination cases, uniform illumination can not be acquired even with large number of fly-eyes pieces. This feature of fly-eyes illumination should be pay good attentions when dealing with non-symmetrical illumination cases. Another feature of fly-eyes illumination is that discrete angular distribution instead of continuous angular distribution of output light is acquired, and this discrete angular pattern varies with numerical aperture of the incoming light. This may be a bad feature for microscope with fly-eyes illumination, but this is a good feature for projection. With these derived mathematical expressions, guidelines for the application of fly-eyes illumination can be found and a deep view into the fly-eyes illumination can be acquired.