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

Glued diffraction optical elements with broadband and a large field of view

High diffraction efficiency is an important requirement for hybrid diffractive-refractive optical systems with a wide field of view. The issue is that diffractive optical elements cannot maintain high diffraction efficiency across a designed waveband and range of incident angles simultaneously. Glued diffractive optical elements (GDOEs) consist of two single-layer diffractive elements, and optical adhesives are presented to address the problem. Two diffractive optical elements are glued together to reduce the straylight scattered into unwanted diffraction orders. The parameters of diffractive optical elements are optimized to achieve broadband high diffraction efficiency and modulation transfer function over a wide-incident-angle range. The GDOEs enable the system to realize a diffraction efficiency of over 90% when the incident angle is no more than 58°. Through gluing two single-layer diffractive optical elements together, we can minimize the inner reflection and refraction. Diffraction efficiency losses can be compensated by the optical adhesives layer, and image quality can be improved. Our design method could make possible the use of diffraction elements in different kinds of optical systems.

Comprehensive polychromatic integral diffraction efficiency sensitivity to tilt error for multilayer diffractive optical elements with oblique incidence

Oblique incidence is the general working state for multilayer diffractive optical elements (MLDOEs) in an imaging optical system. The polychromatic integral diffraction efficiency (PIDE) is very sensitive to the incident angle. Therefore, it is necessary to analyze the effect of tilt error on diffraction efficiency/PIDE with oblique incidence. The theoretical model of the relationship between the diffraction efficiency and tilt error with oblique incidence is presented, and the effect of tilt error on diffraction efficiency/PIDE is analyzed. The analysis model of comprehensive PIDE for a certain range of incident angles and the tilt error for MLDOEs is established. The simulation results showed that the comprehensive PIDE is sensitive to tilt angle with oblique incidence, and the tolerance of the tilt error angle can be determined by the comprehensive PIDE. The tilt error tolerance is furthermore investigated with decenter error based on the maximum of comprehensive PIDE. The method and results can be used to guide the tolerance formulation of tilt error for MLDOEs in hybrid optical systems.

Tolerance analysis on decenter error of multilayer diffractive optical elements based on polychromatic integral diffraction efficiency

The decenter error can determine the polychromatic integral diffraction efficiency (PIDE) over a broad wave band of hybrid optical systems and further the imaging quality. The mathematical model of the relationship between the decenter error and the PIDE of multilayer diffractive optical elements (MLDOEs) is presented, and the expressions are derived based on phase delay of diffractive optical elements for both normal and oblique incident situations. Finally, the sensitivity of PIDE to the decenter error for MLDOEs used in a long-infrared wave band with a material combination of ZNS-ZNSE is analyzed, and then the decenter error tolerance is proposed to ensure high PIDE over a broad wave band as well as diffraction efficiency at the designed wavelengths. The analysis methods and results could be useful for guiding the decenter error of MLDOEs in hybrid optical systems for optical engineers.

Optimal design of depth-scaling error for multilayer diffractive optical elements with oblique incidence

The mathematical analytic models of the relationship between depth-scaling error and diffraction efficiency/polychromatic integral diffraction efficiency (PIDE) for multilayer diffractive optical elements (MLDOEs) with oblique incidence are presented. A method for optimal design of the depth-scaling error for MLDOEs with consideration of comprehensive PIDE working within a range of incident angle is established. The effect of depth-scaling error on diffraction efficiency and PIDE of MLDOEs working in the visible wavelength with oblique incidence is analyzed. For the MLDOEs working within the range of incident angle 0-20°, the maximum comprehensive PIDE is 98.24%, and the optimal relative depth-scaling error is -6.55%. The analytic method and conclusion provide a theoretical basis for the determination of manufacturing tolerance of depth-scaling error for MLDOEs with oblique incidence.

Tolerance analysis of multilayer diffractive optics based on polychromatic integral diffraction efficiency

Multilayer diffractive optical elements (MLDOEs) can achieve high diffraction efficiency for broadband wavelength. Polychromatic integral diffraction efficiency (PIDE) is the key concern for evaluating diffraction efficiency over the waveband. The modulation transfer function of a hybrid refractive-diffractive optical system is directly affected by the PIDE. The relationship between PIDE and continuous manufacturing errors for microstructure heights and periodic widths of MLDOEs is studied theoretically in this paper, and an example of MLDOEs is discussed in the visible waveband. The analysis results can be used for manufacturing error control in microstructure heights and periodic widths.

Analysis of grating doublets for achromatic beam-splitting

Achromatic beam-splitting grating doublets are designed for both continuous phase and binary phase gratings. By analyzing the sensitivity to lateral shifts between the two grating layers, it is shown that continuous-profile grating doublets are extremely difficult to fabricate. Achromatic grating doublets that have profiles with a constant first spatial derivative are significantly more resistant to lateral shifts between grating layers, where one design case showed a 17 times improvement in performance. Therefore, binary phase, multi-level phase, and blazed grating doublets perform significantly better than continuous phase grating doublets in the presence of a lateral shift between two grating layers. By studying the sensitivity to fabrication errors in the height of both grating layers, one grating layer height can be adjusted to maintain excellent performance over a large wavelength range if the other grating layer is fabricated incorrectly. It is shown in one design case that the performance of an achromatic Dammann grating doublet can be improved by a factor of 215 if the heights of the grating layers are chosen to minimize the performance change in the presence of fabrication errors.