In this paper, we discuss some light diffraction phenomena with a simple quantum theory. Firstly, the wave function of the free particle in quantum mechanics is used to explain Fraunhofer diffraction of the light at a rectangular aperture, and the result is consistent with the Huygens-Fresnel principle. Secondly, probabilistic wave method is used to analyze the Talbot effect of a two-dimensional grating. The results show that the photons at the Talbot distance and incident photons are described by the same probability wave. Finally, Talbot effect is used to measure the wavelength of incident light.
In this paper, we propose a method for measuring the micro-angle based on the 2D grating Talbot effect to generate the moiré fringe period. Firstly, the measurement principle of the micro rotation angle of the 2D grating and the characteristics of the 2D grating Talbot imaging are analyzed. And then the 2D grating is measured by the Moiré fringe generated by the Talbot image. Based on this, we derive the calculation formula of the angle, and analyze the accuracy of this method of measuring angle. The method of generating moiré fringes by Talbot imaging has the advantages of higher precision, more flexibility and convenience in measuring the rotation angle than stacking two directly.
In this part, to improve fill factor of microlens array, we designed a new type of square-aperture planar microlens array
which is used for collecting and transferring optical information efficiently. By lithographic ion-exchange and a special
technology to remove the 1.0 micron layer of titanium on the glass substrate, square-aperture planar microlens array is
buried in the substrate and the fill factor of microlens array are larger than 98%. Each microlens unit of the array is
square and has an aperture size of 0.2mm with the excellent capabilities of external stress and temperature. At last, many
optical feature parameters of square-aperture planar microlens array are tested and analyzed, and the experimental results
show that good performance can be used farther in studies and tests later.
Ion thermal diffusion theory was applied to analyze the influence on numerical aperture and focal length of planar square
aperture microlens array (PMLA). Moreover, numerical aperture and focal length with different ion-exchanging time but
the same size of mask aperture were measured experimentally. Then, we measured the longitudinal and transverse
spherical aberration by the method of parallel light incidence and emergent light pupil and improved the aberration of
square-aperture PMLA by annealing treatment. Experiment results show that the spherical aberration is decreased
obviously after annealing process. Meanwhile, imaging resolution is also improved more greatly. PMLA optical system
with continuously adjustable focal length was proposed, which was made up of two pieces of square aperture PMLA and
an aspherical lens and focal length can be adjusted continuously just by precisely adjusting the distance between the two
pieces of square aperture PMLA.
We fabricated a single-layer rotundity PMLA with the photolithography and ion-exchanging technique whose
parameters is developed in experiment. The theory show that the multiple imaging is obtained by both single-layer
PMLA and double-layer PMLA while the comprehensive imaging is obtained only by double-layer PMLA. The imaging
condition of comprehensive imaging for double-layer PMLA is analyzed that the magnification must be equal to 1 in this
paper. The ray trajectory equation of PMLA is accord with rotation-symmetric model, and the paraxial optical properties
of PMLA is obtained by ABCD law. At last, the location parameter of comprehensive imaging is obtained according to
the imaging condition.
Gradient-index lens arrays are important elements for many optical systems. In some systems, the higher space factor is needed. That is to say, the area of receiving light should be enhanced and the loss of light information be decreased. However, this can be realized by changing the shape of lens.
In this work, thermal ion-exchanging technology was introduced as a method to generate gradient refractive-index distributions of hexagonal aperture microlens arrays. As important elements for many optical systems, this irregular microlens arrays can provide very high filling factor which is more than 95 percent and deduce the loss of optical information. We apply the ion-exchanged technique and photolithography to fabricate this irregular microlens arrays, for the first time to our knowledge. The aim of the research is to fabricate this irregular microlens arrays. Fabrication process includes three steps: first, mask with irregular figure is programmed and fabricated; then with photolithographic technology, the figure of mask is transferred to the glass substrate; At last, ion-exchanged process is needed. The experimental results show that good performance can be obtained through this new type lens and the high filling factor is satisfied. Moreover, the experimental index distribution of hexagonal aperture lens is gradient distribution. Therefore, the research on the irregular microlens arrays has an important meaning in application, and this new type microlens array is useful for some systems in which the loss of light information need to be reduced.
In many applications, one repeatedly encounters the problem of laser beam shaping. Shaping laser beam means converting an incident wave front into a desired wave front in the output plane. Superresolution technology can be used for achieving smaller spot than an Airy spot which is the limit of resolution of optical system caused by diffraction. In this work, superresolution technology is extended for laser beam shaping. The aim of the research is to design a new phase-only superresolving element by using local direct search optimization algorithm. The results show that better superresolving performances of our phase elements are obtained compared with those of phase plates of references. The phase element we design is a new type varying in discretely continuous way and is regarded as a hybrid combination of continuous and discrete phase type, whose phase distribution is composed of two parts: the first part is a continuous phase profile; the second part is a constant phase step. The phase steps of this phase plate are different in the different zones. More importantly, it is possible that desired flat-top wave front is obtained by using this design. Therefore, this design provides a novel tool for laser beam shaping.
There are three types of superresolving pupil filters in the optical systems, namely, amplitude type, phase-only type and amplitude-phase type. Among them, phase-only filter has received more attention because of its higher diffractive efficiency than others. The superresolving continuous phase filters were reported in Optics Letters in 2003 by Daniel M. de Juana et al. In this work, a new type of phase-only superresolving pupil filters, varying in discretely continuous way, is presented, whose phase distribution includes two parts: the first part is a sine function, that is, a continuous phase profile; the second part is a constant term, which can be different in the different range of the filter. The goal of the research is to find better results than the superresolving continuous phase filters. From the numerical results, we can see that this type filters can provide higher superresolving performance than the continuous phase filters. This filter with discrete continuous phase zones is also useful for analyzing the performance of a discrete phase filter illuminated with a continuous wavefront. Therefore, although this phase-only superresolving pupil filters are difficult to fabricate at present, the research on this type pupil has an important meaning both in theory and application.