Chung Ki Hong

Pixel-size-maintained image reconstruction of digital holograms on arbitrarily tilted planes by the angular spectrum method

We present an effective method for the pixel-size-maintained reconstruction of images on arbitrarily tilted planes in digital holography. The method is based on the plane wave expansion of the diffraction wave fields and the three-axis rotation of the wave vectors. The images on the tilted planes are reconstructed without loss of the frequency contents of the hologram and have the same pixel sizes. Our method shows good results in the extreme cases of large tilting angles and in the region closer than the paraxial case. The effectiveness of the method is demonstrated by both simulation and experiment.

Rotation error correction by numerical focus adjustment in tomographic phase microscopy

The tomographic imaging technique in digital holography is improved and applied to the measurements of the refractive index distributions of two kinds of optical fiber. They are reconstructed from a set of quantitative phase maps obtained with a digital holographic method as the object is rotated for 180 deg. The errors of the phase maps caused by the defocusing due to the unwanted shift of the object relative to the rotation axis are corrected by numerical focus adjustment. The tomographic images of the fiber samples show the effectiveness of our method.

Interframe intensity correlation matrix for self-calibration in phase-shifting interferometry

A new method of estimating reference phase shifts in phase-shifting interferometry is proposed. The reference phase shifts are determined from a matrix that represents the interframe intensity correlation (IIC) of phase-shifted interferograms. The root-mean-square error of intensity measurement is automatically obtained from the smallest eigenvalue of the IIC matrix. The proposed method requires only four interferograms, unlike others, and can extract phase shifts reliably even from interferograms without well-defined fringes, such as speckle patterns. In typical conditions, reference phase shifts and wave-front phases can be determined with an accuracy of lambda/6310 and lambda/150, respectively. The validity of the method is tested by comparing it with other methods in experiments and simulations.

Least-squares phase estimation with multiple parameters in phase-shifting electronic speckle pattern interferometry.

We have developed an accurate and robust phase-estimation method in phase-shifting electronic speckle pattern interferometry. Unlike other methods that assume a constant phase within a fitting window, our method treats the phase variation with a gradient. A cost function that can utilize the information of pixel positions is formulated on the basis of a least-squares criterion. Powells iteration method is applied to it to derive the phase and its gradient. An automatic consistency-checking routine and an algorithm that improves the initial guess of the iteration are developed for severe situations with large noise and steep phase variations.

Phase-contrast microscopy by in-line phase-shifting digital holography: shape measurement of a titanium pattern with nanometer axial resolution

Precision phase-contrast imaging has been achieved with in-line phase-shifting digital holographic microscopy. The complex amplitude of the object field on the charge-coupled device plane is measured by the phase-shifting method with a self-calibration algorithm, and the magnified object image is reconstructed with a plane wave expansion method. The phase fluctuation in the blank image without sample is 1.30 deg and the three-dimensional shape of a titanium phase test pattern is measured with an accuracy of 5.51 nm (corresponding to the phase resolution of 3.63 deg), which are better than those of off-axis systems.

3-Dimensional Micro-Structure Inspection by Phase-Shifting Digital Holography

We have developed a holographic microscope for the inspection of the 3-dimensional structure of opaque objects. It is based on the phase-shifting digital holography. Digital holography has several characteristics such as free focusing, flexible magnification, and variable viewing angle that can not be shared by other methods. Phase-shifting technique is employed to contour the surface of an opaque micro-object quantitatively. A Michelson-type interferometer is configured as a part of the microscope in such a way that high numerical aperture and compactness can be obtained. We present several results of micro-object measurements and visualization of 3-dimensional structure. Introduction Three-dimensional (3-D) microscopy technique is in great demand in the fields of microelectro-mechanical systems and biology. Conventional optical microscope is subject to the limitation in depth of field, where focusing is adjusted by mechanical movement of a part in measurement system. For quantitative measurement of 3-D micro-structures, white-light scanning interferometry and scanning confocal microscopy have been developed [1,2]. These methods need time-consuming scanning in the direction of optic axis or in the lateral directions. Phase-shifting digital holography [3] has several advantages for 3-D inspection of objects. Adjustment of focus, magnification, viewing angle variation and wave-front aberration correction are carried out flexibly by numerical processing [4-7]. In this paper we report a configuration of a reflection-type holographic microscope. Principles of image formation and reconstruction are discussed briefly. Techniques for the aberration compensation and the scale calibration are presented. Capability of high-quality 3-D imaging is demonstrated. Phase-shifting digital holography In phase-shifting holography (PSH) holograms are recorded by a CCD. The complex amplitude of the object wave at hologram plane is extracted by phase shift analysis. Using diffraction formula, the complex amplitude at the image plane is calculated numerically [4]. Figure 1 shows the basic setup of PSH. The object beam is reflected or transmitted by a specimen. The reference beam reflected by the phase-shifting mirror, which is controlled by a computer, forms spherical or plane wave passing

Photoelectron energy shift induced by microfocused x rays in micrometer-thick insulating layers

The temporal changes of the kinetic energy spectra of photoelectrons emitted from micrometer-thick insulating layers, SiO2, and photoresist layers, were investigated with microfocused soft x rays in soft x-ray spectromicroscopy. The energy spectra of the insulators shifted up to several tens of electronvolts toward lower energies within seconds of the initial exposure. The amount of the energy shift depended on the thickness of the insulators. For the photoresist insulator, which was susceptible to radiation damage, the energy shift then decreased as the exposure time increased. The main cause of this decrease is attributed to the increase of conductivity by the x-ray-induced chemical state change of the insulator along the x-ray path. It was also demonstrated that by choosing appropriate time and energy in detecting photoelectrons the spectromicroscopy could be used as a depth probe of the conducting microstructures covered by insulating layers.

Illumination-angle-scanning digital interference holography for optical section imaging

We propose and experimentally demonstrate a new (to our knowledge) digital holographic method to reconstruct section images of objects with wavelength-dependent reflectivity. A number of holograms of an object are taken as the illumination angle of the laser beam with a specific wavelength is changed in regular intervals. The complex object fields reconstructed from the holograms are numerically superposed to show the image of a sliced section of the object, whose position and thickness can be chosen arbitrarily. By changing the wavelength of the illumination beam, wavelength-dependent section images can be obtained with our method.

Three Dimensional Shape Measurement of a Micro Fresnel Lens with In-line Phase-shifting Digital Holographic Microscopy

An in-line phase-shifting digital holographic microscopy system was constructed by inserting a conventional microscope in the object arm of a Mach-Zehnder interferometer. It was used to measure the three dimensional shape of a micro Fresnel lens. It was also shown that both the lateral and the axial resolutions of the in-line phase-shifting system using a self-calibration algorithm were superior to those of the best off-axis system.

MAXIMUM-LIKELIHOOD PHASE ESTIMATION IN PHASE-SHIFTING ELECTRONIC SPECKLE PATTERN INTERFEROMETRY AND ITS COMPARISON WITH LEAST-SQUARES ESTIMATION

The least-squares phase-fitting method, developed recently without any statistical justification, extracts an almost noiseless phase directly from the distribution of the intensities of phase-shifted speckle interference patterns [ C. K. Hong , Opt. Lett.20, 931 (1995)]. We present another method that can do the same by using the statistically well-established maximum-likelihood algorithm. Numerical simulations show that the precision of the maximum-likelihood estimate is better than that of the least-squares method by 19% and that its precision essentially achieves the one given by the Cramer–Rao lower bound. The limitations of the two methods subject to the phase variation within a fitting window are also studied.