Zernike Phase Contrast Method Research Articles

Wavefront sensing and control in space-based coronagraph instruments using Zernike’s phase-contrast method

Future space telescopes with coronagraph instruments will use a wavefront sensor (WFS) to measure and correct for phase errors and stabilize the stellar intensity in high-contrast images. The HabEx and LUVOIR mission concepts baseline a Zernike wavefront sensor (ZWFS), which uses Zernike's phase contrast method to convert phase in the pupil into intensity at the WFS detector. In preparation for these potential future missions, we experimentally demonstrate a ZWFS in a coronagraph instrument on the Decadal Survey Testbed in the High Contrast Imaging Testbed facility at NASA's Jet Propulsion Laboratory. We validate that the ZWFS can measure low- and mid-spatial frequency aberrations up to the control limit of the deformable mirror, with surface height sensitivity as small as 1 pm, using a configuration similar to the HabEx and LUVOIR concepts. Furthermore, we demonstrate closed-loop control, resolving an individual DM actuator, with residuals consistent with theoretical models. In addition, we predict the expected performance of a ZWFS on future space telescopes using natural starlight from a variety of spectral types. The most challenging scenarios require ~1 hr of integration time to achieve picometer sensitivity. This timescale may be drastically reduced by using internal or external laser sources for sensing purposes. The experimental results and theoretical predictions presented here advance the WFS technology in the context of the next generation of space telescopes with coronagraph instruments.

Self-visualization of transparent microscopic objects in optical glasses under the conditions of the thermal self-action of an illuminating laser beam

We demonstrate the process of adaptive self-visualization of small-scale transparent objects and structures in weakly absorbing optical glasses (a glass plate made of K8 and an NS-1 neutral density filter) placed in the Fourier plane of the optical system under the conditions of thermal self-action of the illuminating laser beam. The process is based on the ideology of the classical Zernike phase contrast method. The process is implemented at the level of power of radiation of the illuminated object varying from several milliwatts to tens of watts in the visible and IR spectral ranges. The conducted experiments indicate that the visualization takes place in all glasses and optical elements fabricated from them at an appropriate level of the radiation power.

Performance analysis of quantitative phase retrieval method in Zernike phase contrast X-ray microscopy*Supported by the State Key Project for Fundamental Research (2012CB825801), National Natural Science Foundation of China (11475170, 11205157 and 11179004) and Anhui Provincial Natural Science Foundation (1508085MA20).

Since the invention of Zernike phase contrast method in 1930, it has been widely used in optical microscopy and more recently in X-ray microscopy. Considering the image contrast is a mixture of absorption and phase information, we recently have proposed and demonstrated a method for quantitative phase retrieval in Zernike phase contrast X-ray microscopy. In this contribution, we analyze the performance of this method at different photon energies. Intensity images of PMMA samples are simulated at 2.5 keV and 6.2 keV, respectively, and phase retrieval is performed using the proposed method. The results demonstrate that the proposed phase retrieval method is applicable over a wide energy range. For weakly absorbing features, the optimal photon energy is 2.5 keV, from the point of view of image contrast and accuracy of phase retrieval. On the other hand, in the case of strong absorption objects, a higher photon energy is preferred to reduce the error of phase retrieval. These results can be used as guidelines to perform quantitative phase retrieval in Zernike phase contrast X-ray microscopy with the proposed method.

Calibration of quasi-static aberrations in exoplanet direct-imaging instruments with a Zernike phase-mask sensor

Context. Several exoplanet direct imaging instruments will soon be in operation. They use an extreme adaptive optics (XAO) system to correct the atmospheric turbulence and provide a highly-corrected beam to a near-infrared (NIR) coronagraph for starlight suppression. The performance of the coronagraph is however limited by the non-common path aberrations (NCPA) due to the differential wavefront errors existing between the visible XAO sensing path and the NIR science path, leading to residual speckles in the coronagraphic image. Aims. Several approaches have been developed in the past few years to accurately calibrate the NCPA, correct the quasi-static speckles and allow the observation of exoplanets at least 1e6 fainter than their host star. We propose an approach based on the Zernike phase-contrast method for the measurements of the NCPA between the optical path seen by the visible XAO wavefront sensor and that seen by the near-IR coronagraph. Methods. This approach uses a focal plane phase mask of size {\lambda}/D, where {\lambda} and D denote the wavelength and the telescope aperture diameter, respectively, to measure the quasi-static aberrations in the upstream pupil plane by encoding them into intensity variations in the downstream pupil image. We develop a rigorous formalism, leading to highly accurate measurement of the NCPA, in a quasi-linear way during the observation. Results. For a static phase map of standard deviation 44 nm rms at {\lambda} = 1.625 {\mu}m (0.026 {\lambda}), we estimate a possible reduction of the chromatic NCPA by a factor ranging from 3 to 10 in the presence of AO residuals compared with the expected performance of a typical current-generation system. This would allow a reduction of the level of quasi-static speckles in the detected images by a factor 10 to 100 hence, correspondingly improving the capacity to observe exoplanets.

Computer analysis of two-dimensional images in the Zernike phase contrast method for hard X rays

The problems of the numerical simulation of two-dimensional images in the Zernike phase contrast method in hard X rays are analyzed. Calculations are performed for experimental conditions typical of third-generation synchrotron radiation sources (ESRF, APS, Spring-8, etc.). Schemes are considered where the focusing elements are a refracting lens and a zone plate and the phase-shifting element is situated at the point of the source image. It is shown that the refracting lens allows better resolution than the zone plate. A technique similar to ptychography can be successfully applied to improve the quality of the images obtained by the Zernike phase contrast method.

Theoretical analysis of the possibilities of Zernike phase contrast method in hard X rays for nondestructive imaging of micropipes in a silicon carbide single crystal

The possibilities of using Zernike phase contrast in hard X rays for imaging micropipes in a silicon carbide single crystal are analyzed by numerical simulation. Calculations are performed for the experimental conditions characteristic of third-generation synchrotron radiation sources. A scheme is considered where the focusing element is a parabolic refracting lens and the phase-shifting element is mounted at the point of the source image. It is shown that micropipe cross sections by a beam with a longitudinal diameter reaching 10 μm are imaged by the lens without distortions. At the same time, the lens makes it possible to magnify the image several tens of times. The cross sections that are significantly elongated along the beam are imaged with artifacts; however, their structure can also be recovered. It is shown that polychromaticity of radiation does not significantly affect the object imaging.

Research on wavefront-sensing for improving receiver efficiency in turbulence atmosphere

In the air-to-ground optical communication system, not only must we considerate the impact of beam pointing, but also the wavefront turbulence the atmosphere brings to the beam can not be ignored. This paper simply analyses the influence of the atmosphere turbulence on air-to-ground optical communication, and reforms the traditional adaptive optics(AO) system using the famous Zernike phase contrast method, which can makes it be applied to the air-to-ground optical communication system to correct the turbulence of the wavefront and improve the receiving efficiency and the system performance. In the end of this paper, the simulation of this method described above to detect phase is presented.

Computer simulation of the zernike phase contrast in hard x-ray radiation using refractive lenses and zone plates

Computer simulation of an experiment on imaging transparent (phase) microobjects using the Zernike phase contrast method under hard X-ray radiation has been performed. The beam parameters typical for synchrotron radiation sources of the third generation were used in calculations. Both a refracting lens and a zone plate have been considered as a focusing element. The phase shifting quarter-wave plate is located at a spot of the point source image. The results of calculations have shown that the method can be successfully used for objects with the sizes greater than 0.1 μm along and 1 μm across the beam. It has been shown that the contrast is caused not only by increasing the intensity within the shadow of the objects, but also by decreasing the intensity in the area beyond the objects, which is necessary to retain the integral intensity.

On-sky performance of the Zernike phase contrast sensor for the phasing of segmented telescopes

The Zernike phase contrast method is a novel technique to phase the primary mirrors of segmented telescopes. It has been tested on-sky on a unit telescope of the Very Large Telescope with a segmented mirror conjugated to the primary mirror to emulate a segmented telescope. The theoretical background of this sensor and the algorithm used to retrieve the piston, tip, and tilt information are described. The performance of the sensor as a function of parameters such as star magnitude, seeing, and integration time is discussed. The phasing accuracy has always been below 15 nm root mean square wavefront error under normal conditions of operation and the limiting star magnitude achieved on-sky with this sensor is 15.7 in the red, which would be sufficient to phase segmented telescopes in closed-loop during observations.

Zernike phase contrast cryo-electron tomography

Cryo-tomography in the electron microscope is unique in its ability to provide high-resolution, three-dimensional structural information about cells, organelles and macromolecules in a nearly native, frozen-hydrated state. However, the phase-contrast imaging method used in conventional cryo-electron tomography fails to faithfully represent the full range of structural features in such specimens. Only certain features are recorded with adequate contrast, and overall contrast is low. The recently developed Zernike phase contrast method has the potential to solve this problem, and here we apply it for the first time to cryo-electron tomography. The new method has uniform transfer characteristics for a wide range of spatial frequencies, leading to improved overall signal-to-noise ratio and raising the prospects of higher resolution and quantitative representation of specimen densities in the reconstructed tomograms.

Complex Observation in Electron Microscopy: VI. Comparison of Information Transfer Reliability between Zernike Complex Observation and Transport of Intensity Equation Method

A transmission electron microscopic (TEM) scheme to reconstitute wavefronts of electrons scattered from objects, which was termed as complex observation (COBS), has been successfully introduced. COBS is based on a complex combination of two orthogonal TEM experiments of the conventional (bright-field) and Zernike phase contrast method, both of which are relying on the interference phenomenon for the phase recovery. Recently, another class of phase recovery, the non-interference method often called as the Transport of Intensity Equation (TIE) method, has been proposed. TIE rather relies on the change of the optical energy or intensity in the direction of wave transfer. We report the methodological comparison between COBS and TIE, which has been carried out with TEM simulations and by using a new index, ITR, which was introduced in a previous paper for the comparison of principal aspects of microscopic schemes. TEM simulation has been clarified the preference of COBS in the image quality. This has been also confirmed quantitatively by using ITR, where the drawback of TIE comes to more visible. TIE inherently requests a differential operation to close the formulation, which is actually problematic for images including noise components. Signals in the low and high frequency regions are both seriously influenced by the noise, which results in a rather low resolution image for objects with a low dose limit such as biological samples.

Hard X-ray phase-contrast microscope for observing transparent specimens

A hard X-ray transmission imaging microscope has been in use at the beamline BL24XU of SPring-8. It makes use of a phase zone plate made of tantalum as its X-ray lens, and is capable of imaging the structure as fine as 125-nm line-and-space pattern. The Zernike's phase-contrast method has been implemented to the microscope with phase plates made of gold. The photon energy was tuned to 12 keV just above the L3 absorption edge of gold (11.9 keV) in order to increase the image contrast. Polystyrene micro particles as transparent specimens were imaged clearly in the opposite image contrast with phase plates to shift the phase of the central order spectra in the back focal plane of the objective by one-quarter and three-quarters of a period while the absorption contrast image showed little image contrast. Performance of the newly developed phase zone plate has been tested and it was confirmed that the structure as fine as 60-nm line-and-space pattern was able to be imaged.

Halo Reduction Technique in Phase Contrast Microscopy

A new phase contrast microscopy technique has been developed which achieves halo reduction by applying an apodization to the Zernike phase contrast method. In this technique, a new apodized phase plate is placed at the back focal plane of the objective. This plate consists of a quarter wave phase shift ring conjugated of the illuminating aperture, which has a 25#x0025; transmittance, and a pair of adjacent rings having 50#x0025; transmittance. The developed technique yields the highest resolution images without a bluish hue effect ever achieved in phase contrast microscopy.

Artifact Halo Reduction in Phase Contrast Microscopy Using Apodization

A new phase contrast microscopy technique for halo reduction is proposed. This technique is based on an apodization method combined with the Zernike phase contrast method. Although it has been a diflicult theoretical problem, the proposed technique achieves halo reduction by considering angles of diffraction and phase differences. The technique utilizes an apodized phase plate consisting of a quarter wave phase shift ring with a 250/0 transmittance, and a pair of adjacent rings, which have 500/0 transmittance. This element is placed at the back focal plane of the objective. The result is startling, halo reduced images of phase objects providing enhanced inner details. Key word~: phase contrast microscopy, apodization, halo, apodized phase plate, angle of diffraction, phase difference

Lossless light projection

A new technique for energy-preserving phase-only light projection is demonstrated. The phase-only encoding is based on an extension of the Zernike phase-contrast method into the domain of full-range [0; 2pi ] phase modulation, breaking the usual small-phase-angle limitation. Controlling the spatial average value of the input-phase pattern and choosing appropriate phase retardation at the phase-contrast filter yield pure-phase-based image formation. Experimental results demonstrate close to 90% energy efficiency. Output intensity levels with magnitudes more than 3.5times that of the input intensity level were measured in the brightest regions of the projected images.

Phase contrast image synthesis

A new method is presented for synthesizing arbitrary intensity patterns based on phase contrast imaging. The concept is grounded on an extension of the Zernike phase contrast method into the domain of full range [0; 2π] phase modulation. By controlling the average value of the input phase function and by choosing appropriate phase retardation at the phase contrast filter, a pure phase to intensity imaging is accomplished. The method presented is also directly applicable in dark field image synthesis.

Spherical aberration correction using a liquid-crystal spatial-light modulator in off-axis electron holography

One can correct spherical aberration in a transmission electron microscope by using a newly developed aberration-correction method involving off-axis electron holography. In this method, a liquid-crystal spatial-light modulator (LC SLM) is employed during the holographic reconstruction step to compensate for spherical aberration. Application of this method to high-resolution off-axis electron holograms of fine gold particles is presented. The phase distribution of the corrected object wave is visualized by the Zernike phase-contrast method carried out with the same LC SLM.

A CO2 laser tangential imaging system for CDX-U (abstract)

In a previous paper [R. Nazikian and B. Grek, Rev. Sci. Instrum. 61, 2899 (1990)], it was shown that tangential imaging provides a powerful new technique for rendering two-dimensional images of local density fluctuations in toroidal plasma devices. The technique consists of projecting a CO2 laser beam tangent to magnetic field lines at the plasma midplane and using phase contrast or other related optical methods for imaging line integral density fluctuations. In this paper we present recent progress in the development of such an imaging system for CDX-U. The interferometer makes use of a novel variation on the Zernike phase contrast method for detecting phase variations impressed on laser beams propagating through random media. This work supported by Department of Energy contract No. DE-AC02-76-CHO-3073.

Testing optical surfaces by the method of the caustic using a phase-stripe as spatial filter

The use of a phase stripe as spatial filter in the measurement of optical surfaces by the method of the caustic was studied. This is an adaptation of Zernike's phase contrast method to the zonal measurement of optical surfaces by the method of the caustic. We analyzed three path differences introduced by the stripe lambda/4, lambda/3, and lambda/2. The best results may be expected for lambda/3, and with a phase stripe of this path difference a mirror was tested. The mean square deviation between several measurements with this spatial filter was 0.0076lambda.

Phase Difference Microscopy

I HAVE read with much interest the description by Mr. O. W. Richards of his own and his colleagues' recent work on Zernike's phase contrast method. Everyone who is interested in the microscopical observation of living cells should be grateful to him for having once again directed attention to its value as applied to microscopy. It possesses the advantage over ordinary trans-illumination that fine unstained structural detail is seen in greatest contrast by focusing exactly on the specimen, so that we may expect a closer geometrical correspondence between the appearance seen and what is 'really there'.