Orthogonal crossed gratings, or two-dimensional (2D) gratings are key optical elements in plane optical encoders. In this paper, Scanning Dammann lithography (SDL) was implemented to fabricate gold-coated 2D gratings by stepping and scanning a 2D air-bearing stage and rotating Dammann gratings. A displacement measurement interferometer (DMI) was applied to monitor the 2D stage which ensured the positioning accuracy of exposing. A series of experiments by varying the exposure dose were conducted. The atomic force microscope (AFM) results indicted the duty cycle changed with the exposure dose. A 2D gold-coated grating with a size 100*100mm was also fabricated. Since it is straightforward to extend the size of the substrate up to hundreds of millimeters, SDL is a promising method to fabricate large-sized 2D gratings with controllable duty cycle.
In this paper, we propose a high-density grating interferometry system, which can be applied to measure displacement on the nanometer precision. We make use of the optical subdivision module to improve the measurement resolution which is better than the traditional one. The core part of the whole system is a grating with high-density of 1780 lines/mm and long-range of 100mm*100mm. The apparatus adopts a symmetrical structure to reduce the error resulting from environmental disturbance. The system provides a novel measurement technique to improve the grating interferometry. The experimental results show that the grating interferometer system has good stability, and the in-situ measurement error is within ±5 nm for a long time. The grating interferometer can measure the short distance displacement of 30 nm and can control the error within ±2 nm. The measurement of the distance of 10 mm can control the error within ±20 nm. The results proves the feasibility of our proposed improved.
Grating theory is normally designed for nano/microoptics applications. If we consider the further smaller size, we might enter the area of picometer optics. Although it seems picometer optics might be the frontier of developing nanooptics devices into the next step, it is hard to make picometer optical devices previously. We will report a series of three works that can lead us into the picometer scale. The first is to fabricate high-density gratings whose periods can be controlled to be slightly different in picometer range, which is done by rotating Dammann grating in a microrad angle for achieving the grating period continuously tuned in picometer scale. The second is to propose carrier pico-grating array for measuring the distances of the moving grating, which can be done in picometer accuracy. The third is to measure the wavefront of two-beam interferences in picometer accuracy, which is far beyond the current normal laser interferometer. Initial experimental results demonstrated that the wavefront has been measured with 250pm linear phase difference, which is impossible to obtain with the traditional laser interferometer. Taking consideration of these picometer works together, we believe that picometer optics should come with these picometer optical tools further extended in the near future.
The 38.5 W spectral combined beam of a 19-element 940 nm diode laser bar has been demonstrated in the spectral beam combining experiment by using a Beam Transformation System (BTS). The outputs had a diffraction-limited beam quality in the fast axis and M2=10.5 in the slow axis. Spectral beam combining was achieved by using an external cavity including a transmission diffraction 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.
To produce large scale gratings by Scanning Beam Interference Lithography (SBIL), a light spot containing grating pattern is generated by two beams interfering, and a scanning stage is used to drive the substrate moving under the light spot. In order to locate the stage at the proper exposure positions, the period of the Interference pattern must be measured accurately. We developed a set of process to obtain the period value of two interfering beams at picometer level. The process includes data acquisition and data analysis. The data is received from a photodiode and a laser interferometer with sub-nanometer resolution. Data analysis differs from conventional analyzing methods like counting wave peaks or using Fourier transform to get the signal period, after a preprocess of filtering and envelope removing, the mean square error is calculated between the received signal and ideal sinusoid waves to find the best-fit frequency, thus an accuracy period value is acquired, this method has a low sensitivity to amplitude noise and a high resolution of frequency. With 405nm laser beams interfering, a pattern period value around 562nm is acquired by employing this process, fitting diagram of the result shows the accuracy of the period value reaches picometer level, which is much higher than the results of conventional methods.
Displacement laser interferometers and grating interferometers are two main apparatus for the micron-nanometer displacement measurement over a long range. However, the laser interferometers, whose measuring scale is based on the wavelength, are very sensitive to the environment. On the contrast, the grating interferometers change the measuring scale from wavelength to grating period, which is much stable for the measurement results. But the resolution of grating interferometer is usually lower than that of laser interferometer. Therefore, further investigation is needed to improve the performance of grating interferometer. As we known, the optical subdivision is a main factor that affects the measurement resolution. In this paper, a grating interferometer with high optical subdivision is presented based on the Littrow configuration. We mainly use right angle prisms accompanied with plane mirrors to make the measuring lights diffracted by the grating scale for many times. An optical subdivision factor of 1/24 can be obtained by this technique. A main difficulty of this technique is that the grating scale should be with high diffraction efficiency. Fortunately, the measuring light is incident on the grating scale at the Littrow angle, the grating scale can be designed with very high efficiency easily in this condition. Compared with traditional grating interferometers, this kind of grating interferometer can greatly increase the measuring resolution and accuracy, which could be widely used in nanometer-scale fabrications and measurements.
A grating interferometer is presented based on the quasi-Littrow configuration. We mainly use a plane mirror to make the measuring light reflect and diffract between the mirror and grating scale for several times. According to the grating Doppler shift, the more times that measuring light diffracted, the higher optical subdivision can be obtained. As an example, a grating interferometer with an optical subdivision factor of 1/12 is designed. This work provides a technique to increase the resolution of the grating interferometer, which should be interesting for high precision measurement.
Optical encoders and laser interferometers are two primary solutions in nanometer metrology. As the precision of encoders depends on the uniformity of grating pitches, it is essential to evaluate pitches accurately. We use a CCD image sensor to acquire grating image for evaluating the pitches with high precision. Digital image correlation technique is applied to filter out the noises. We propose three methods for determining the pitches of grating with peak positions of correlation coefficients. Numerical simulation indicated the average of pitch deviations from the true pitch and the pitch variations are less than 0.02 pixel and 0.1 pixel for these three methods when the ideal grating image is added with salt and pepper noise, speckle noise, and Gaussian noise. Experimental results demonstrated that our method can measure the pitch of the grating accurately, for example, our home-made grating with 20μm period has 475nm peak-to-valley uniformity with 40nm standard deviation during 35mm range. Another measurement illustrated that our home-made grating has 40nm peak-to-valley uniformity with 10nm standard deviation. This work verified that our lab can fabricate high-accuracy gratings which should be interesting for practical application in optical encoders.
A new method of single-track absolute position encoding based on spatial frequency of stripes is proposed. Instead of using pseudorandom-sequence arranged stripes as in conventional situations, this kind of encoding method stores the location information in the frequency space of the stripes, which means the spatial frequency of stripes varies with position and indicates position. This encoding method has a strong fault-tolerant capability with single-stripe detecting errors. The method can be applied to absolute linear encoders, absolute photoelectric angle encoders or two-dimensional absolute linear encoders. The measuring apparatus includes a CCD image sensor and a microscope system, and the method of decoding this frequency code is based on FFT algorithm. This method should be highly interesting for practical applications as an absolute position encoding method.