As system performance continues to improve at higher resolutions, it becomes increasingly important to establish standards for imaging degradation caused by optical windows. In this study, random surface shapes were simulated on large area optical windows with peak-to-valley (P-v) values of 0.25, 0.5, and 1.0 λ. Modulation Transfer Function (MTF) values were derived for 1,000 cases per P-v value using Monte-Carlo simulations. The specifications achieved a surface accuracy of 0.5 λ and a parallelism of 0.01 mm. MTF measurements showed that the system MTF was 13.5% prior to the installation of the optical window, and 13.1% after installation. This indicates a degradation rate of approximately 3%.

In this investigation, we propose a simple and effective lateral shearing interferometer based on a polarization grating. In the lateral shearing device, an incident beam is split into two beams by a polarization grating, and the returning beams can be laterally shifted after reflecting off a flat mirror and passing through the polarization grating again. These two beams are not only laterally shifted, but also their polarization states are orthogonal to each other as circular polarizations. With a single image obtained by a pixelated polarization CMOS camera, the proposed LSI can obtain the phase map corresponding to the x-sheared interferogram, and the other phase map can be calculated from another single image obtained by 90° rotation of the shearing device. Then, the original wavefront corresponding to the surface figure of the specimen can be reconstructed by wavefront reconstruction algorithms. In the experiments, various wavefronts generated by concave mirrors and a deformable mirror were measured and compared with those of a commercial Shack-Hartmann sensor.

A spectral-domain interferometer with dual reference paths and orthogonal polarization states to avoid measurement errors when interference signals overlap is proposed and realized. In our previous study, by using dual reference mirrors, two inherent problems of the spectral-domain interferometer, the non-measurable range and the directional ambiguity problem, were successfully solved. However, because of the overlap of interference signals, the absolute distance values were distorted. In this study, the polarization states of beams from two reference paths were made orthogonal to eliminate the interference signal between them, so that the overlap can be essentially avoided. First, we performed a numerical simulation on the measurement error with respect to the degree of superposition of the interference signals. Simulation results show that with the previous method the measurement error can be up to approximately 1 μm within the overlap region, but the proposed method drastically reduced this error to below 100 nm. Then, the proposed method was experimentally realized and verified. In conclusion, the proposed method can measure the absolute distances without the inherent problems as well as the measure errors caused by the overlap of the interference signals.

Industrial robots are widely used for part manufacturing besides simple task (welding, assembly). A parallel kinematic machine (PKM) with extending axes have been utilized in large volume machining because of their adequate stiffness and agility. Parallelism error in the PKM with an extending axis causes deterioration of dimensional accuracy of machined parts. This paper proposes a technique for compensating the parallelism error through measurement of the squareness error between the PKM with its extending axes using a laser interferometer. The four squareness errors are estimated to reduce the parallelism errors. The squareness error is calculated by measuring linearity of the extending axis and the PKM moving axis, and through the measurement of diagonal displacement error and position dependent geometric errors. Compensation of the parallelism error was done by transforming the basic coordinate system of the PKM. The parallelism error was significantly reduced from 0.735 to 0.022 mm and further verified experimentally.

Spectrally resolved interferometry (SRI) is an attractive technique to measure absolute distances without any moving components. In the spectral interferogram obtained by a spectrometer, the optical path difference (OPD) can simply be extracted from the linear slope of the spectral phase. However, SRI has a fundamental measuring range limitation due to maximum and minimum measurable distances. In addition, SRI cannot distinguish the OPD direction because the spectral interferogram is in the form of a natural sinusoidal function. In this investigation, we describe a direction determining SRI and propose the optimal conditions for determining OPD direction. Spectral phase nonlinearity, caused by a dispersive material, effects OPD direction but deteriorates spectral interferogram visibility. In the experiment, various phase nonlinearities were measured by adjusting the dispersive material (BK7) thickness. We observed the interferogram visibility and the possibility of direction determination. Based on the experimental results, the optimal dispersion conditions are provided to distinguish OPD directions of SRI.

In this investigation, we describe a metrological technique for surface and thickness profiles of a silicon (Si) wafer by using a 6 degree of freedom (DOF) stitching method. Low coherence scanning interferometry employing near infrared light, partially transparent to a Si wafer, is adopted to simultaneously measure the surface and thickness profiles of the wafer. For the large field of view, a stitching method of the sub-aperture measurement is added to the measurement system; also, 6 DOF parameters, including the lateral positioning errors and the rotational error, are considered. In the experiment, surface profiles of a double-sided polished wafer with a 100 mm diameter were measured with the sub-aperture of an 18 mm diameter at 10x10 locations and the surface profiles of both sides were stitched with the sub-aperture maps. As a result, the nominal thickness of the wafer was 483.2 μm and the calculated PV values of both surfaces were 16.57 μm and 17.12μm, respectively.