Polarized structured illumination microscopy using polarization gratings for optical sectioning: publisher's note.

This publisher's note contains corrections to Appl. Opt.62, 7373 (2023)APOPAI0003-693510.1364/AO.502290.

Polarized structured illumination microscopy using polarization gratings for optical sectioning.

In this investigation, we describe polarized structured illumination microscopy based on polarization gratings to generate a stable polarized illumination pattern in an extensive area. The visibility of the illumination pattern is immediately calculated by using a polarizing pixelated camera, and the 3D surface profile of the specimen can be successfully reconstructed. Moreover, a polarization grating pair was used to reasonably eliminate the unexpected pattern caused by the polarization grating itself. To experimentally characterize the system performance, a step height standard specimen was measured. Moreover, the axial response for the visibility of the illumination pattern was discussed with the consideration of the spectral bandwidth of the source and the spatial coherence of incident light.

Surface figure measurement tool based on a radial shearing interferometer using a geometric phase lens with various spherical wavefronts.

We describe a compact radial shearing interferometer based on a geometric phase lens as a surface figure measurement tool. Based on the polarization and diffraction characteristics of a geometric phase lens, two radially sheared wavefronts are simply generated, and the surface figure of a specimen can be immediately reconstructed from the radial wavefront slope calculated with four phase-shifted interferograms obtained from a polarization pixelated complementary metal-oxide semiconductor camera. In order to increase the field of view, moreover, the incident wavefront is adjusted according to the shape of the target, which allows the reflected wavefront to become planar. By the combination of the incident wavefront formula and the measurement result by the proposed system, the whole surface figure of the target can be instantaneously reconstructed. As the experimental result, the surface figures of various optical components were reconstructed at the extended measurement area with less than 0.78 µm deviations, and it was confirmed that the radial shearing ratio was fixed independent of the surface figures.

High-precision polarized dual low-coherence scanning interferometry for rapid step height measurements.

In this investigation, we propose a polarized dual low-coherence scanning interferometer. The spatial phase-shifting technique and the concept of the dual low coherence are adopted to overcome the scanning conditions of typical low-coherence scanning interferometers and reduce the measurement time. In the proposed interferometer, the scanning interval is not critical because the visibility and the phase are immediately obtained during a scanning procedure, and the whole scanning distance can be significantly reduced by the dual low coherence. To verify the system performance, the surface profiles of a plane mirror and a step height specimen were measured, and it was confirmed that the whole scanning distance was reduced 10 times without any scanning conditions.

Recent Progress on Optical Tomographic Technology for Measurements and Inspections of Film Structures.

In this review, we present the recent progress on film metrology focused on the advanced and novel technologies during the last two decades. This review consists of various technologies and their measurement schemes to provide the inspiration for understanding each of the measurement principles and applications. In the technology and analysis section, several optical techniques used in film metrology are introduced and described with their benefits and limitations. The temporal, spatial and snapshot measurement schemes of optical film metrology are introduced in the measurement scheme section, and finally, the prospect on optical film metrology will be provided and discussed with the technology trend.

Radial shearing dynamic wavefront sensor based on a geometric phase lens pair.

A radial shearing dynamic wavefront sensor is theorized and experimentally verified. The proposed sensor is based on a geometric phase lens pair that generates two radially sheared wavefronts. A polarization pixelated camera instantaneously obtains polarization-multiplexed phase maps from a single acquired image using a spatial phase-shifting technique. Experimental tests applied several wavefront shapes with a deformable mirror. The results were compared with a Shack-Hartmann wavefront sensor to evaluate the performance.

Spherical wavefront measurement on modified cyclic radial shearing interferometry.

We propose a radial shearing interferometric approach to measure spherical wavefronts as both of the reflective and transmissive optical configurations. The modified cyclic radial shearing interferometer uses a single lens in the optical layout, which can conveniently adjust the radial shearing ratio between two shearing spherical wavefronts, and the use of a polarization camera enables to reconstruct the wavefront by a single image. The wavefront mapped onto the camera plane can be identified and quantified throughout an optimized wavefront reconstruction algorithm. In the experiments, plano-convex lenses and concave mirrors were used to generate spherical wavefronts, and the proposed system was able to reconstruct the surface figures after system characterization and calibration. Further investigations were performed to evaluate the system measurement accuracy by the radius of curvature comparison with design value and a commercial Shack-Hartmann wavefront sensor.

Polarized imaging interpreter for simultaneous clocking metrology of multiple objects.

A polarized imaging interpreter to simultaneously measure rotational angles of multiple objects is proposed and experimentally verified. Based on the multiplexed optical configuration using a polarization pixelated camera, the proposed sensor has the unique feature to precisely monitor the standard and the non-standard clocking motions in static or dynamic applications at once.

Single-shot spectrally resolved interferometry for the simultaneous measurement of the thickness and surface profile of multilayer films.

We present a single-shot spectrally-resolved interferometry for simultaneously measuring the film thickness and surface profile of each layer of a patterned multilayer film structure. For this purpose, we implemented an achromatic phase shifting method based on the geometric phase using the polarization characteristics of the light and obtained four phase-shifted interferograms in the spectrally-resolved fringe pattern at the same time by combining a pixelated polarizing camera with an imaging spectrometer. As a result, we could simultaneously measure the reflectance and phase of the sample over a wide wavelength range with a single measurement. To evaluate the validity of the proposed method, we measured a patterned five-layer film specimen and compared our measurement results with those from commercial instruments, an ellipsometer and a stylus profiler, respectively. We confirmed the results matched each other well.

Vision chromatic confocal sensor based on a geometrical phase lens.

A vison chromatic confocal sensor used to monitor the location of a measured point is proposed and experimentally verified. To induce chromatic aberration of the sensor, a geometrical phase lens is adopted and is also used as a beam splitter. Near the geometrical phase lens, a focused beam is used for the chromatic confocal sensor, and a diverging beam is used for imaging of the specimen. In the experiment, the performance of the proposed system was verified with regard to distance sensing and the capability of monitoring the measured points. The measuring range was approximately 10 mm, and the repeatability was 0.4 µm when a geometrical phase lens with a 75 mm focal length was used.

Motionless Polarizing Structured Illumination Microscopy.

In this investigation, we propose a motionless polarizing structured illumination microscopy as an axially sectioning and reflective-type device to measure the 3D surface profiles of specimens. Based on the spatial phase-shifting technique to obtain the visibility of the illumination pattern. Instead of using a grid, a Wollaston prism is used to generate the light pattern by the stable interference of two beams. As the polarization states of two beams are orthogonal with each other, a polarization pixelated CMOS camera can simultaneously obtain four phase-shifted patterns with the beams after passing through a quarter wave plate based on the spatial phase-shifting technique with polarization. In addition, a focus tunable lens is used to eliminate a mechanical moving part for the axial scanning of the specimen. In the experimental result, a step height sample and a concave mirror were measured with 0.05 µm and 0.2 mm repeatabilities of step height and the radius of curvature, respectively.

Spectrally resolved polarizing interferometer for single-shot line profiling.

In this investigation, we describe a spectrally resolved polarizing interferometer to modify the typical spectrally resolved interferometer based on the Fourier method, which has a dead zone caused by the minimum measurable range. By use of a polarization pixelated CMOS camera, which enables us to obtain spatially phase-shifted spectral interferograms, the spectral phase can be extracted with a single image, and the proposed interferometer can obtain a line profile of a specimen at once. By the nature of phase-shifting technique, moreover, the directions of the measured distances can be identified, and the measuring range is extended to twice that of the typical spectrally resolved interferometer. In the experimental results, the measuring range was 104 µm, and the capability to obtain a line profile of a specimen with a single image was confirmed. For 3D surface profiling, lateral scanning was adopted, and the measurement results were compared with the result of the Fourier method.

Diverging cyclic radial shearing interferometry for single-shot wavefront sensing.

In this investigation, we describe a simple cyclic radial shearing interferometer for single-shot wavefront sensing. Instead of using the telescope lens system used in typical radial shearing interferometry, a single lens is used to generate two diverging radial shearing beams. This simple modification leads to the advantages of conveniently adjusting the radial shearing ratio, compactness of the system, and practical ease of alignment. With the aid of a polarization pixelated CMOS camera, the spatial phase-shifting technique is used to extract the phase with a single image. The most important feature is the fringe contrast enhancement by reducing the aberrations caused by the complicated optical system even though an incoherent light is used. The experimental results show the fringe contrast enhancement is at least 0.1 better than that of the conventional method, and the wavefronts are properly reconstructed with less than 0.071λ root-mean-squared wavefront error regardless of the coherence of the light.

A compact high-precision periodic-error-free heterodyne interferometer.

We present the design, bench-top setup, and experimental results of a compact heterodyne interferometer that achieves picometer-level displacement sensitivities in air over frequencies above 100 MHz. The optical configuration with spatially separated beams prevents frequency and polarization mixing, and therefore eliminates periodic errors. The interferometer is designed to maximize common-mode optical laser beam paths to obtain high rejection of environmental disturbances, such as temperature fluctuations and acoustics. The results of our experiments demonstrate the short- and long-term stabilities of the system during stationary and dynamic measurements. In addition, we provide measurements that compare our interferometer prototype with a commercial system, verifying our higher sensitivity of 3 pm, higher thermal stability by a factor of two, and periodic-error-free performance.

Advances in optical metrology and instrumentation: introduction.

Optical measurement and characterization are two of the pillars of metrology. The ability to measure precisely with high dynamic range and accuracy betters our understanding of nature and the universe. In this feature issue, we present a collection of articles that delves into the fundamental techniques used to advance the field.

Single-shot freeform surface profiler.

We propose a novel and simple method of single-shot freeform surface profiler based on spatially phase-shifted lateral shearing interferometry. By the adoption of birefringent materials, the laterally shearing waves are simply generated without any bulky and complicated optical components. Moreover, the phase maps that lead to the 3D profile of the freeform surface can be instantly obtained by the spatial phase-shifting technique using a pixelated polarizing camera. The proposed method was theoretically described and verified by measuring several samples in comparison to the measurement results with a well-established stylus probe.

Single-Shot Imaging of Two-Wavelength Spatial Phase-Shifting Interferometry.

In this investigation, we propose an effective method to measure 3D surface profiles of specimens with single-shot imaging. Based on the two-wavelength interferometric principle and spatial phase-shifting technique using a polarization pixelated camera, the proposed system can not only rapidly measure the phase, but also overcome the 2π-ambiguity problem of typical phase-shifting interferometry. The rough surface profile can be calculated by the visibility of the interference fringe and can compensate for the height discontinuity by phase jumps occurring in a fine height map. An inclined plane mirror and a step height specimen with 9 µm were used for the validation of capability of measuring continuously smooth surface and large step heights. The measurement results were in good agreement with the results of typical two-wavelength interferometry.

Rigorous single pulse imaging for ultrafast interferometric observation.

We discuss how to realize rigorous single pulse imaging using a fiber mode-locked laser for the purpose of ultrafast interferometric observation of fast varying dynamic objects. Sub-picosecond pulses are readily picked up in synchronization with the camera operation, allocating one pulse per frame, but rigorous ultrashort single pulse imaging is disturbed by the accumulation of amplified spontaneous emission (ASE) over the exposure time of the camera. Here, we propose four distinct methods to eliminate the ASE-accumulated disruption in the ultrashort optical gating by pulse interferometry and then evaluate their merits and limitations individually by experiments. The proposed four methods are referred to respectively as the time averaged phase modulation, unbalanced pulse overlapping, tandem pulse picking, and second harmonic generation.

Single-shot characterization of multi-film structures based on combined spectral interferometry and spatially recorded spectroscopic ellipsometry.

In this investigation, we propose an improved combined scheme with spectral interferometry and spatially recorded spectroscopic ellipsometry to measure surface height and film thicknesses at once in real time. Instead of rotating polarizing optical components, a spatial phase retarder, which consists of spatially rotating liquid crystal arrays, is used to obtain the ellipsometric spectral data from a single image. In addition, interferometric configuration is combined to collect the surface height information in the same image. The spatial phase retarder can be characterized by the phase retardation and the rotation angle of the liquid crystal during the calibration procedure. In the experiments, single-layered and multi-layered film specimens were measured to verify the measurement capability of the proposed system, and it was confirmed that the measurement results were in good agreement with the provided reference values.

High-speed polarized low coherence scanning interferometry based on spatial phase shifting.

In this investigation, we describe polarized low coherence scanning interferometry (PLCSI) to enhance the measurement speed based on the spatial phase shifting technique by using a polarized CMOS camera. In every scanning step, the visibility of the correlogram can be directly extracted by spatial phase shifting. PLCSI does not need any scanning conditions such as a scanning step size smaller than that determined by the Nyquist sampling limit and equidistant scanning step, which restrict the measurement speed of the typical low coherence scanning interferometry (LCSI). The measurement data can also be significantly reduced due to the larger scanning step size. PLCSI can be comparable to confocal scanning microscopy in the view of monitoring visibilities. In the experiments, three types of specimens such as a plane mirror, a concave mirror, and a step height specimen were measured by PLCSI with various scanning step sizes, and it was confirmed that the surface profiles were successfully reconstructed. Moreover, the compensation technique of the surface profile, precisely determined by the phase information, was also discussed.