No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Design of diffractive optical elements based on several simple formulae
Abstract
A new method for designing diffractive optical elements (DOEs), based on the diffraction theory is reported. The method does not require complex computation and programming. The DOE can be easily designed according to simple formulas and has higher imaging accuracy. The DOE diffraction coefficient depends on taking the complex amplitude transmission.
... With binary encoding, a modernization of the expanded Kirk-Jones method with a spatial carrier frequency [11] relying on the phase jump width variation can be used: ...
... The numerical simulation carried out in [4] showed that the linear relation between the phase jump width and the amplitude encoded in equation (11) gave somewhat superior results compared with the nonlinear relation in equation (12). ...
A binary diffractive optical element (1500 pixels × 1500 pixels, diameter 4.5 mm) is designed by partial encoding and fabricated by direct electron beam writing in SiO2. Two conjugate hyper-geometric laser modes are generated using the fabricated element. The root-mean-square transverse intensity deviation of the experimental from theoretical diffraction pattern, determined within a circle of radius 1 mm, is below 13%.
The majority of the beam splitters for three beam tracking in commercial DVD pickup employ lamellar phase gratings, which already provides sufficient efficiency. However, for a pickup with all diffractive elements, the power budget becomes more critical, and a higher efficiency of the beam splitter is required. In this paper, we have investigated and will present the influence of the desired energy ratio between the zeroth order central beam to the first order side beam on the total efficiency of the beam splitter. The simulation based on scalar diffraction theory shows that the total efficiency of a lamellar phase grating will drop as the ratio decrease, which can be improved by employing a more sophisticated surface relief. The equal-side triangular profile has been investigated as a solution and the geometrical size of the profile has been optimized for several desired energy ratio. For a low cost fabrication process with photolithography, the total efficiency loss due to quantization with different quantization levels of the triangular surface relief has been estimated with scalar diffraction theory. This paper is concluded with a table of optimal phase level for a given energy ratio and desired minimum total efficiency with the consideration of fabrication cost.
A diffractive optical elements (DOEs), permits to change a wave front by means of diffraction. The proposed method has the advantage of not requiring complex computation and programming. In particular the designed process is made without computer iterative methods. The DOE, implemented by the proposed algorithm, consists of cells of equal size. Each cell is subdivided into appropriate parts. The average phase of these parts is related to the phase of the complex amplitude. The DOE phase can be easily computed according to simple formulas. In the paper designing phases and numerical simulation are reported. In particular the effect of the DOE structure quantization is considered.
The limited efficiency of diffractive optical elements is an important
consideration in their design and application. These elements,
fabricated using lithographic techniques, have very high theoretical
diffraction efficiencies when analyzed using first-order scalar
analysis. However, assumptions made in this scalar approach limit its
accuracy for high frequency diffractive structures, such as those
encountered in fast diffractive lenses. Fabrication limitations also
reduce the physically achievable diffraction efficiency. This paper will
discuss alternatives to the conventional scalar analysis technique and
review how fabrication constraints can be incorporated into the design
approach to realize improvements in diffraction efficiency.
The phase optimization of a quantized kinoform by the genetic algorithm is discussed. Because the genetic algorithm inherently deals with discrete values, the quantized phase of the kinoform can be easily estimated. The periodicity of the discrete Fourier transform for the 2D Fourier kinoform enables us to perform the crossover process, which is one of the processes in genetic algorithms, without concern of a spatial bandwidth of the kinoform. We introduce a step-quantization method for the multilevel kinoform. Improvements are shown to be significant with this method in computer simulations. The optically reconstructed image agrees well with the calculated one.
An algorithm is presented for the rapid solution of the phase of the complete wave function whose intensity in the diffraction and imaging planes of an imaging system are known. A proof is given showing that a defined error between the Thimated function and thecorrect function must decrease as the algorithm iterates. The problem of uniqueness is discussed and results are presented demonstrating the power of the method.
Dual-wavelength multiple beam splitters (DWMBS's) are designed to split a dual-wavelength beam into two beam arrays, one for each of the two wavelengths. These two beam arrays may have either the same dimension and structure or different dimensions and structures, depending on applications. We present results of our computer simulations for a 1 x 5 DWMBS that exhibits one-dimensional diffraction efficiency and uniformity of 83.8% and 98.4%, respectively, for a wavelength of 514.5 nm and of 85.1% and 99.0%, respectively, for a wavelength of 632.8 nm.