Tingyu Zhao

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.

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.

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.

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.

Field depth extension of 2D barcode scanner based on wavefront coding and projection algorithm

Wavefront coding (WFC) used in 2D barcode scanners can extend the depth of field into a great extent with simpler structure compared to the autofocus microscope system. With a cubic phase mask (CPM) employed in the STOP, blurred images will be obtained in charge coupled device (CCD), which can be restored by digital filters. Direct methods are used widely in real-time restoration with good computational efficiency but with details smoothed. Here, the results of direct method are firstly filtered by hard-threshold function. The positions of the steps can be detected by simple differential operators. With the positions corrected by projection algorithm, the exact barcode information is restored. A wavefront coding system with 7mm effective focal length and 6 F-number is designed as an example. Although with the different magnification, images of different object distances can be restored by one point spread function (PSF) with 200mm object distance. A QR code (Quickly Response Code) of 31mm X 27mm is used as a target object. The simulation results showed that the sharp imaging objective distance is from 80mm to 355mm. The 2D barcode scanner with wavefront coding extends field depth with simple structure, low cost and large manufacture tolerance. This combination of the direct filter and projection algorithm proposed here could get the exact 2D barcode information with good computational efficiency.

The research of underwater imaging based on the wavefront coding system

Current research on the underwater imaging often needs particular techniques. Since the specificity of the underwater imaging system, it must overcome the impact of the turbulent and turbid of the water. In this paper we present a new application of the wavefront coding (WFC) system in the underwater imaging. Wavefront coding system is a two-step imaging system, by using a cubic phase mask with optimized parameters; we get the defocus-insensitive intermediate image in the imaging plane. Then the final sharp image can be obtained by deconvoluted the intermediate image with the point spread function (PSF). Initially the wavefront coding system is introduced to extent the depth of the field of the optical system and the allowance of the system can be great improved by using the optimized cubic phase mask. Because of the defocus-insensitive property, this system can eliminate the aberration brought by the turbulent of the water. The deconvolution can improve the imaging quality by deblurring intermediate image and reduce the impact brought by the turbid of the water. In order to get excellent result, we propose to use the global generalized minimal residual method as the deconvolution algorithm. Antireflective boundary conditions (BCs) are considered to eliminate ringing effect, and Kronecker product approximation is introduced to reduce the computation consumption. This method can give excellent deconvolution result. There is little ringing effect on the image border and little vibration on the edge. Theory analysis and the experiment show that this is an effective system in the underwater imaging. It is an economical system.

Strehl ratio analysis for the wavefront coding system

Strehl ratio is an important aspect in evaluating the performance of the optical imaging system. Even in wavefront coding imaging systems, Strehl ratio also plays an important role. It can be used to evaluate the sensitivity of phase masks to aberrations, and it can also be added as the penalty in the optimization of phase mask parameters to make sure that the noise gain of the intermediate image recovery is not too large. However the conventional Strehl ratio analyses are only suitable for the optical system with a small amount of aberration, while the wavefront coding imaging system is an optical system with a large aberration, the most of which are the characteristic aberrations introduced by the phase plate. In this paper, the approximate expressions of Strehl ratio are derived for the wavefront coding system with phase plates of free order and free type. These expressions show a good coincidence with the numerical ones. Based on these expressions, the impact of the phase masks order can be analyzed. Besides, the sensitivity of Strehl ratio to all kinds of aberrations can also be analyzed for the wavefront coding system with phase plates. Phase plates of different types are shown to be sensitive to aberrations of different types, and the impact of the aberration order can also taken into account. At last, some advice is given for taking Strehl ratio as one of the performance aspects while choosing phase plates.