This research proposes a feedback method to adjust the dual-beam exposure system with spherical collimation lenses to achieve gratings with low spacing error. Through theoretical analysis and numerical calculation, it is proved that the interference aberration can be analyzed with the Zernike polynomials and the adjustment errors can be estimated according to the linear relationship between the errors and the polynomial coefficients. Moreover moving the substrate along its normal is proposed to decrease the spacing error but keep the grating’s period unchanged. In the experiments, the wavefront measurement results of the ± 1st orders are used to deduce the spacing error. Based on the feedback adjustment method, the grating with a spacing error of 0.03 λ within 70 mm × 70 mm is fabricated with the collimation lenses of 0.6 λ spherical aberration.

Analysis and minimization of spacing error of holographic gratings recorded with spherical collimation lenses.

A Lloyd’s mirror interferometer is widely used in holographic lithography to fabricate gratings. Adjustment errors of the interferometer and manufacturing errors of optical elements will both influence the wavefront aberration of a grating. We analyze their influence and propose a method to optimize the wavefront aberration. The correctness of the simulation and the feasibility of the adjustment method are experimentally verified. With this method, low-aberration gratings can be fabricated in a Lloyd’s mirror interferometer.

Wavefront aberration of plane diffraction gratings fabricated in a Lloyd's mirror interferometer

A single collimating lens based dual-beam exposure system for fabricating long-period grating

Large-sized gratings are essential optical elements in laser fusion and space astronomy facilities. Scanning beam interference lithography is an effective method to fabricate large-sized gratings. To minimize the nonlinear phase written into the photo-resist, the image grating must be measured to adjust the left and right beams to interfere at their waists. In this paper, we propose a new method to conduct wavefront metrology based on phase-stepping interferometry. Firstly, a transmission grating is used to combine the two beams to form an interferogram which is recorded by a charge coupled device(CCD). Phase steps are introduced by moving the grating with a linear stage monitored by a laser interferometer. A series of interferograms are recorded as the displacement is measured by the laser interferometer. Secondly, to eliminate the tilt and piston error during the phase stepping, the iterative least square phase shift method is implemented to obtain the wrapped phase. Thirdly, we use the discrete cosine transform least square method to unwrap the phase map. Experiment results indicate that the measured wavefront has a nonlinear phase around 0.05 λ@404.7nm. Finally, as the image grating is acquired, we simulate the print-error written into the photo-resist.

Image grating metrology using phase-stepping interferometry in scanning beam interference lithography

In this work, an optical system with large diameter off-axis parabolic lenses was adopted to achieve diffraction gratings by laser interference exposure. The diffraction wavefront aberration caused by temperature variations was simulated using ZEMAX. Through theoretical analysis and optical simulation, it is proved that the diffraction wavefront aberration of holographic grating caused by the pinhole’s location errors (it is assumed that when the displacement of pinhole exists along one axis, the locations of the pinhole along the other two orthogonal axes are in a state of precise adjustment ) is much larger when the displacement occurs along z axis than along the other two axes, and the diffraction wavefront aberration is the smallest when the displacement occurs along x axis. If the ambient temperature changes by 1 degree, the PV value is 0.0631λ when the location of the pinhole changes by 0.121mm along z axis, 0.0034λor 0.0672λ when the location of the pinhole changes by 0.002mm along x axis or 0.03mm along y axis. To reach the diffraction limit (that means the PV value is 0.25λ), the decentering value of the pinhole along z axis should be less than 0.0341mm. In conclusion, the position error along z axis is an important factor to influence the PV value of diffraction grating, and the effect of temperature on the PV value of diffraction grating can be neglected.

Influence of temperature on the optical system with large diameter off-axis parabolic lenses

Large size pulse compression grating (PCG) with needs high adjusting precision in the light path of PCG fabrication. Note that the longitudinal error is the most error source of diffraction wavefront aberration of grating. It is difficult from conventional light path regulation to obtain such small longitudinal regulative error. A simple and practical method for regulating light path of PCG with big size is introduced. Rotate the grating fabricated by conventional light path adjustment and place it on the original recorded plane. The real grating and the imaginary one produced by two constructive beams interference overlap to produce the moire fringe pattern. Generally speaking, conventional regulation generates longitudinal error that results in cirques. Regulating the pinhole till Moire fringes become parallel and straight, and then backtrack with half of the regulating quantity, which is called Moire fringe method (MFM). With that, the problem that longitudinal precision of conventional light path adjustment is low is solved. To begin with the imaging formula of holographic lens, the principle of MFM is deduced theoretically. From results generated by ZEMAX software, the diffraction wavefront aberration of grating can be reduced to the least by MFM effectively. Proceeding with the relationship between optical system of holographic grating and the diffraction wavefront aberration of grating, the aberration of moire fringes obtained by analyzing the deviation of the fringes from parallel straight lines is about twice as the diffraction wavefront aberration of grating by reference to primary aberration theory.

Jianhong Wu

Papers

New method for the fabrication of pulse compression grating