The importance of wavefront sensing has significantly increased in applications of adaptive optics for astronomy and EUV lithography. Wavefront sensors are also widely used to test optical components of smartphone cameras, as well as virtual reality (VR) and augmented reality (AR) devices. Two conventional methods of measuring wavefront shapes are with a Shack-Hartmann or a pyramid wavefront sensing technique. These sensors have a high sensitivity and robust response, but lack in lateral resolution and dynamic range. Alternative to wavefront metrology, an optical interferometer can be used to improve the lateral resolution of measurements. Several interferometric principles have been proposed and experimentally verified such as point diffraction interferometry, digital holography, lateral shearing interferometry, and radial shearing interferometry.
Optical interferometry has been traditionally used in wavefront sensing, and especially shearing interferometers were adopted to reconstruct the wavefront of light with the advantage of no reference light. A lateral shearing interferometer (LSI) can reconstruct the wavefront using so called, x- and y-sheared interferograms with the aid of zonal and modal reconstruction algorithms. Compared to radial shearing interferometry (RSI), LSI does not have to confirm concentricity between two sheared wavefronts, which restricts the measurement of wavefronts without rotational symmetry.
One of the main considerations in LSI is the phase extraction from the interferograms because two laterally sheared wavefronts are typically generated by a fixed shear plate. Even though the spatial carrier technique can be used, the additional calculations with two-dimensional Fourier transformation and spatial filtering deteriorate the phase. In order to apply the phase shifting technique, a grating pair was used and the phase shifted interferograms were obtained by the movement of the grating. Recently, a polarization-pixelated camera and a birefringent plate have been adopted for a single shot LSI based on spatial phase shifting technique. On the other hand, another issue in LSI is the capability of the lateral shear adjustment according to the various target shapes. For the steep wavefronts, the lateral shear should be small while it is vice versa in plane-like shapes. However, the lateral shear is almost fixed in typical LSI because of the fixed shearing devices, and the system can be bulky when the shearing is implemented by the additional interferometric configurations.
In this investigation, we propose a simple and effective lateral shearing interferometer based on polarization gratings. The proposed LSI consists of a polarization grating (PG), a flat mirror (M) and a polarization-pixelated CMOS camera (PCMOS). As an optical source, a LED with 550 nm center wavelength is used with 10 nm band-pass filter (BPF), and the reflected beam from the specimen is incident to the lateral shearing device. In the lateral shearing device, the incident beam is split into two beams by the PG, and the returning beams can be laterally shifted after reflecting off the flat mirror and passing through the PG again. These two beams are not only laterally shifted, but also their polarization states are orthogonal to each other as circular polarizations. Then, the PCMOS, where a polarizer array with 0°, 45°, 90° and 135° transmission axes is put on the imaging sensor, can obtain four phase-shifted interferograms at once to calculate the phase map based on the spatial phase shifting technique. With a single image obtained by the PCMOS, 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 the 90° rotation of the shearing device. Then, the original wavefront can be reconstructed by the wavefront reconstruction algorithms. As the experimental results, wavefronts generated by a toroidal mirror and cylindrical lenses including concave mirrors and aspheric lenses were successfully measured, and the deviations from the reference shapes were less than 100 nm.
One of the benefits in the proposed LSI is to conveniently adjust the lateral shear distance according to the wavefronts. In case of measuring plane like shapes, the lateral shear distance should be enough large for increasing the signal-to-noise ratio (SNR) to reduce the distortion of the wavefront by experimental noises such as diffraction, speckle and unexpected reflection.