Changxi Xue

Effects of manufacturing errors on diffraction efficiency for multilayer diffractive optical elements

The effect of manufacturing errors on diffraction efficiency for multilayer diffractive optical elements (MLDOEs) used in imaging optical systems is discussed in this paper. The relationship of diffraction efficiency and depth-scaling errors are analyzed for two different cases: the two relative depth-scaling errors change in the same sign and in the opposite sign. For the first condition, the corresponding diffraction efficiency decreases more slowly. The effect of periodic width errors on diffraction efficiency is also evaluated. When the two major manufacturing errors coexist, the magnitude of the decrease of diffraction efficiency is analyzed for MLDOEs. The result can be used for analyzing the effects of the manufacturing errors on diffraction efficiency for MLDOEs.

Optimal design of multilayer diffractive optical elements with effective area method.

The effective area method is described to design high-efficiency multiplayer diffractive optical elements (MLDOEs) with finite feature sizes for wide wave band. This method is presented with consideration of the shield effect between two elements of MLDOEs, and the optimal surface relief heights of MLDOEs are calculated with the effective area method. Then the comparisons of diffraction efficiency and polychromatic integral diffraction efficiency for MLDOEs with different period widths are described and simulated with the effective area method and scalar diffraction theory (SDT). Finally, the design results of MLDOEs obtained by SDT and the effective area method are compared by a rigorous electromagnetic analysis method, specifically, the finite-difference time-domain method. These results show that the limits of SDT for MLDOEs, ascertain and quantify the greatest sources of the diffraction efficiency loss due to the shield effect. The design results of the effective area method can obtain higher polychromatic integral diffraction efficiency than that of the SDT when the period width of MLDOEs is taken into account.

Effect of assembling errors on the diffraction efficiency for multilayer diffractive optical elements

Based on the expression function of diffraction efficiency, and the phase delay function of diffractive optical elements (DOEs), the diffraction efficiency for multilayer diffractive optical elements (MLDOEs) is described with tilt and decenter assembling errors. A mathematical model of the relationship between diffraction efficiency and assembling errors of MLDOEs is proposed to analyze the effect of assembling errors on the diffraction efficiency of MLDOEs. The analyzed results from the mathematical model provide a range of values for the effect of assembling errors on the diffraction efficiency of MLDOEs. Assembling errors are important parameters for hybrid diffractive refractive optical systems, including MLDOEs, and so the proposed model will be useful for guiding the design and fabrication of such optical systems.

Diffraction efficiency sensitivity to oblique incident angle for multilayer diffractive optical elements

The relationship between diffraction efficiency of multilayer diffractive optical elements (MLDOEs) and arbitrary incident angle was numerically analyzed with the effective area method. The method is based on the shield effect between two elements of MLDOEs; a generalized diffraction efficiency formulation was obtained in a wide range of tilt angles, which overcame the limitations of scalar diffraction theory when the period width of MLDOEs is taken into account. A detailed comparison of the proposed effective area method with the scalar diffraction theory is numerically presented for MLDOEs. The validity of the proposed method is verified by comparison with the rigorous electromagnetic analysis method, especially the finite-difference time-domain method. The analysis results show that the shield effect augments with the increase of the incident angles; the effect of incident angles on MLDOEs with finite period widths is more noticeable than that with large period widths.

Diffractively corrected counter-rotating Risley prisms

Using the vector refraction equation and the vector diffraction equation, we obtain the expressions of the direction cosines of the refractive rays for the two wedge prisms, and the direction cosines of the diffractive rays for two wedge grisms, in which diffractive gratings were etched into the prism faces to correct the chromatic aberrations. A mathematical model between the two vector equations is proposed to compare the difference angle chromatic aberrations when the Risley prisms/grisms are rotating at different angles. We conclude that the use of diffractively corrected prisms offers a new method to correct chromatic aberrations in Risley prisms.

Athermalization and thermal characteristics of multilayer diffractive optical elements

A mathematical model to analyze the thermal characteristics of the multilayer diffractive optical elements (MLDOEs) is presented with consideration of the thermal characteristics for the refractive optical elements and single-layer diffractive optical elements. The analysis process of athermalization for MLDOEs by using the opto-thermal expansion coefficient of optical materials is given. Meanwhile, the microstructure heights of surface relief MLDOEs, the optical path difference, and the polychromatic integral diffraction efficiency with the ambient temperature changed are analyzed. The analysis results can be used to guide an athermalization design for the hybrid refractive-diffractive optical systems with MLDOEs.

Evaluation of narcissus for multilayer diffractive optical elements in IR systems

The influence of narcissus effect for multilayer diffractive optical elements (MLDOEs) is evaluated from the viewpoint of diffraction efficiency and the narcissus intensity. A modified paraxial evaluation criterion for the reflected narcissus radiation of MLDOEs has been deduced. A practical 8-12 μm IR optical system designed with one two-layer diffractive element has been given to illustrate the distribution of incident narcissus energy among various diffraction orders in the waveband. The narcissus intensities of the two diffractive surfaces have been calculated for those diffraction orders that have the maximum diffraction efficiency. This method can be used in the process of evaluation and control of the narcissus influence in IR optical systems with MLDOEs.

Calculation and evaluation of narcissus for diffractive surfaces in infrared systems

In infrared optical systems, the narcissus effect for diffractive surfaces should be calculated with specific diffraction orders based on the diffraction efficiency. It is shown in this work that the diffraction order of maximum diffraction efficiency varies with the change of the incident angle and wavelength of the backward-traced narcissus flux. Meanwhile, yni, which is the paraxial evaluation criterion of narcissus intensity for a refractive surface, is modified considering diffraction when a ray passes through diffractive surfaces, and a practical example has been given. The analysis can be used to calculate and control the narcissus intensity in infrared optical systems with diffractive surfaces.

Design and simulation of a superposition compound eye system based on hybrid diffractive-refractive lenses

Compound eyes offer a promising field of miniaturized imaging systems. In one application of a compound eye, superposition of compound eye systems forms a composite image by superposing the images produced by different channels. The geometric configuration of superposition compound eye systems is achieved by three micro-lens arrays with different pitches and focal lengths. High resolution is indispensable for the practicability of superposition compound eye systems. In this paper, hybrid diffractive-refractive lenses are introduced into the design of a compound eye system for this purpose. With the help of ZEMAX, two superposition compound eye systems with and without hybrid diffractive-refractive lenses were separately designed. Then, we demonstrate the effectiveness of using a hybrid diffractive-refractive lens to improve the image quality.

The height error range of multilayer diffractive optical element with consideration of polychromatic integral diffraction efficiency

According to the expression of the phase delay and diffraction efficiency of the diffractive optical elements(DOEs), the expression of diffraction efficiency of multilayer diffractive optical element(MLDOEs) with the height error in fabrication process was described in this paper. We selected the PC and PMMA used usually at optics as substrate material of MLDOEs, and analyze the height error range of multilayer diffractive optical element with consideration of polychromatic integral diffraction efficiency basing on the mathematical analysis model of the relationship between height error and diffraction efficiency for MLDOEs. The range of height error the diffraction efficiency of MLDOEs was given. This model can be used to guide the design and fabrication process of hybrid diffraction refractive optical system for optical engineer.