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 novel method of displacement measurement based on a high density grating pair is proposed. When a laser beam is incident normal to a closely placed high density grating pair, efficiencies of transmission diffraction orders will change periodically along with the relative displacement of the two gratings in the grating period direction. The period of efficiency changing is equal to the grating period, thus measurement of displacement in the grating period direction can be achieved by detecting the power of diffraction orders.
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.
Beam splitters are widely used in various optical modern systems for separating optical wave into different directions. We have proposed a novel slanted grating for beam splitter at the central wavelength of 1550nm, which can be used in the optical communication. With the simulated annealing algorithm, beam splitter slanted grating can be optimized by using the rigorous coupled wave analysis (RCWA). The diffraction process can be analyzed by the simplified modal method. The simplified modal method, without complicated calculation, reduces the difficult diffraction process into a vividly and physical modal. We have derived an analytical expression which can provide an insightful physical description of the simplified modal method for the slanted grating. Compared with the rectangular grating, the slanted grating has the asymmetric physical structure. Therefore, the odd grating mode can also be excited in the slanted grating under normal incidence. The odd grating mode, which only exists in the asymmetric structure, plays the role of breaking the symmetric field distribution in the output plane. The physical analytical expression of mode conversion and coupling for the slanted grating can be obtained to interpretation the asymmetric field distribution. Numerical results obtained by the rigorous coupled wave analysis verified the validity of the simplified modal method. We expect the modal method for the slanted grating set forth in this work should be helpful for the tremendous potential application of the slanted grating.
In this paper, we develop a binocular three-dimensional measurement system using a Dammann grating. A laser diode and a Dammann grating are employed to generate a regular and square laser spot array. Dammann array illuminator is placed between two cameras and narrowband-pass filters are embedded in the project lens to eliminate the interference of background light. During the measurement, a series of laser spot arrays are projected toward the target object and captured by two cameras simultaneously. Similar to stereo vision of human eyes, stereo matching will be performed to search the homologous spot which is a pair of image points resulting from the same object point. At first, the sub-pixel coordinates of the laser spots are extracted from the stereo images. Then stereo matching is easily performed based on a fact that laser spots with the same diffraction order are homologous ones. Because the system has been calibrated before measurement, single frame three-dimensional point cloud can be obtained using the disparity of homologous points by triangulation methods. Finally, three-dimensional point clouds belong to different frame which represent different view of the object will be registered to build up an integral three-dimensional object using ICP algorithm. On one hand, this setup is small enough to meet the portable outdoor applications. On the other hand, measurement accuracy of this system is better than 0.3 mm which can meet the measurement accuracy requirements in most situations.
Femtosecond laser technology is one of the frontiers in the fields of nonlinear optics, advanced manufacturing etc. The method of femtosecond pulse compression is an important research content. To compress the femtosecond pulse, we need to use negative dispersive elements to compensate the positive dispersion of Ti: sapphire crystal and other optical elements. For this purpose, we propose a miniature double-line-density grating pair in which the line density of the second grating is twice of the first one, the output pulse propagates along the way back. The density of the gratings is high, which will have a high diffraction efficiency and can compensate a high GVD ( group velocity dispersion ) in a small distance. The first grating is transmitted and the second one is reflective, the device will not occlude the beam propagation. With the pair of the gratings, the input positive chirped 89fs pulse is neatly compressed into the Fourier transform limited 44fs pulse with no spectral spatial walkoff and dispersion. It can be used for compression in laser cavity or out of the cavity. The gratings are easy to adjust and the structure is simple and compact, which has widespread interest in practical applications.