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.
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.
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 mask's 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.
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.