Laser interference lithography (LIL) is concerned with the use of interference patterns generated from two or several
coherent beams of laser radiation for the structuring of materials. This paper presents the work on the processes based on
resists and direct writing with laser interference lithography. In the work, a four-beam laser interference system was used
as a submicrometer structuring tool in which a high-energy pulsed, frequency-tripled and TM polarized Nd:YAG laser (355 nm) with a coherent length of 3 m, energy power up to 320 mJ/cm2, pulse duration of 8 ns and 10 Hz repetition rate was used as a light source. The experimental results were achieved with 2-beam and 4-beam interference patterning. The processes can be used to define submicron surface relieves in large areas for use in the field of MEMS.
This paper presents a theoretical analysis of formation of 4-beam laser interference patterns for nanolithography.
Parameters of 4-beam interference patterns including the pattern amplitude, period, orientation and uniformity were
discussed. Analytical expressions were obtained for the spatial distribution of radiation of the interfering beams as a
function of their amplitudes, phases, angles of incidence on the sample, and polarization planes with computer
simulation and experimental results.
This paper presents a reference pattern-based two-dimensional (2D) measurement method. In the method, surface structure patterns obtained from a four-beam laser interference lithography (LIL) process were used as reference patterns for 2D measurement. The reference patterns played the role of 2D rulers in the measurement. The nano resolution of the measurement was achieved by feature counting and pattern matching techniques. A statistical analysis indicates that the measurement made by pattern matching has the advantage of averaging noise. For reference pattern-based 2D measurement, the reference patterns can be regular or irregular. This approach is potentially useful for micro and nano manipulation in the processes of assembly, packaging and manufacturing of nano and micro-systems when relative nano positioning accuracy is required.
This paper presents a method for determining the slope and period of oblique and equi-spaced fringes by fringe pattern matching. In the method, two pairs of image patches in two different regions of a fringe pattern are selected for fringe pattern matching, and the phase shift between the fringes in the two selected regions of the fringe pattern is obtained from the two mismatch curves which are calculated from the mismatch function in fringe pattern matching. The slope and period of oblique fringes can be therefore determined using the distance between the two selected regions, the phase shift between the fringes in the regions, and the period of mismatch function with a subpixel resolution. The effect of image patch size on the determination of the slope and period of oblique fringes is also discussed based on a statistical analysis. The statistical analysis, computer simulation and experimentation results have shown that the determination of the slope of oblique and equi-spaced fringes by fringe pattern matching has the advantage of averaging noise due to the region-based matching.
This paper presents the methods of linear interpolation and polynomial curve fitting for achieving sub-pixel resolution phase difference determination by fringe pattern matching. These two methods wee examined by computer simulation and experiment. In computer simulation, the effects of the resolutions of imaging system were also discussed. The computer simulation and experimental result have shown that the method of linear interpolation and that of polynomial curve fitting can both be used to achieve sub-pixel resolution in the measurement of phase difference by fringe pattern matching. The phase difference between fringe patterns is easy to achieve by linear interpolation compared with polynomial curve fitting.
This paper presents a method of displacement measurement that is based on Young's experiment. In the method, the displacement is determined according to the fringe spacing equation from Young's experiment. The method is examined in a fiber-optic interferometer system and a subpixel resolution of measurement is achieved from 100 X 152 pixel image patches using fringe pattern matching together with the polynomial curve fitting method. The effect of the number of discrete grey levels of an image on the accuracy of displacement measurement is also discussed. The computer simulation and experiment have shown that it is possible to measure displacement in a machine vision system in some cases using this method.
This paper presents an algorithm of phase-shifting interferometry with precise phase steps. In the algorithm, the phase steps between the interferograms captured by a CCD camera are taken as unknowns and they are directly determined by fringe pattern matching with subpixel resolution. The algorithm is therefore inherently free from the phase step errors caused by air turbulence, thermal drift, mechanical vibration, miscalibration and nonlinearity of the phase shifter. The computer simulation in the 3D surface measurement has shown that fringe pattern matching is effective in phase-shifting interferometry to find the phase steps from the interferograms with equi-spaced fringe patterns. In addition, this algorithm is potentially useful in the measurement of the physical quantities that are related to optical phase changes such as length and displacement.
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