Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the hologram is then processed using a plane wave in the reconstruction. This physical compensation can be avoided, and several numerical methods exist to retrieve phase contrast images in which the microscope curvature is compensated. Usually, a digital array of complex numbers is introduced in the reconstruction process to perform this curvature correction. Different corrections are discussed in terms of their influence on the reconstructed image size and location in space. The results are presented according to two different expressions of the Fresnel transform, the single Fourier transform and convolution approaches, used to propagate the reconstructed wavefront from the hologram plane to the final image plane.     

Noise suppression and optical sectioning by non-phase-recording interferometry

It has long been known that image plane holography with low-coherence illumination achieves optical sectioning of a volume object. A method is analyzed that is similar to image plane holography, but the interferometric arrangement utilizes the interference between two object-bearing beams instead of the basic object and reference beams.     

Three-dimensional remote sensing by optical scanning holography

A technique is presented by which holograms can be recorded when an object or scene is scanned with an optically heterodyned Fresnel zone pattern. The experimental setup, based on optical scanning holography, is described and experimental results are presented. We apply the scanning holography technique to three-dimensional reflective objects for the first time to our knowledge and address the unique requirements for such a system. We discuss holographic recording and numerical image reconstruction using a system point-spread function (PSF) approach. We demonstrate numerical image reconstruction of experimentally recorded holograms by two techniques: deconvolution with a simulated PSF and an experimentally acquired PSF.     

Effects of quantization in phase-shifting digital holography

We discuss quantization effects of hologram recording on the quality of reconstructed images in phase-shifting digital holography. We vary bit depths of phase-shifted holograms in both numerical simulation and experiments and then derived the complex amplitude, which is subjected to Fresnel transformation for the image reconstruction. The influence of bit-depth limitation in quantization has been demonstrated in a numerical simulation for spot-array patterns with linearly varying intensities and a continuous intensity object. The objects are provided with uniform and random phase modulation. In experiments, digital holograms are originally recorded at 8 bits and the bit depths are changed to deliver holograms at bit depths of 1 to 8 bits for the image reconstruction. The quality of the reconstructed images has been evaluated for the different quantization levels.     

Encrypting three-dimensional information with digital holography

A method for optical encryption of three-dimensional (3D) information by use of digital holography is presented. A phase-shifting interferometer records the phase and amplitude information generated by a 3D object at a plane located in the Fresnel diffraction region with an intensity-recording device. Encryption is performed optically by use of the Fresnel diffraction pattern of a random phase code. Images of the 3D object with different perspectives and focused at different planes can be generated digital or optically after decryption with the proper key. Experimental results are presented.     

Mean and variance of energy reflected from a diffuse object illuminated by radiation with partial temporal coherence

Closed-form integral expressions are developed for the mean and variance of power and energy received from a diffusely reflective object upon illumination by laser radiation with partial temporal coherence. Expressions are presented in dimensionless form and analytic approximations to the integrals are given for signal variations at a receiver caused by fully developed laser speckle. Results are presented in terms of three parameters: the mutual Fresnel number of the receiver and object, the number of longitudinal modes of the illuminating source, and the dimensionless mode spacing of the illuminating source. The calculations assume high light levels and free-space geometry.     

Quantitative space-bandwidth product analysis in digital holography

The space-bandwidth product (SBP) is a measure for the information capacity an optical system possesses. The two information processing steps in digital holography, recording, and reconstruction are analyzed with respect to the SBP. The recording setups for a Fresnel hologram, Fourier hologram, and image-plane hologram, which represent the most commonly used setup configurations in digital holography, are investigated. For the recording process, the required SBP to ensure the recording of the entire object information is calculated. This is accomplished by analyzing the recorded interference pattern in the hologram-plane. The paraxial diffraction model is used in order to simulate the light propagation from the object to hologram-plane. The SBP in the reconstruction process is represented by the product of the reconstructed field-of-view and spatial frequency bandwidth. The outcome of this analysis results in the best SBP adapted digital holographic setup.     

Holography with Light Beams of Finite Spectral Width

The effects of spectral coherence on holographic images have been analysed in terms of the Fresnel-transform formulation of the process of holography. In this paper the case of very rough object or diffuse illumination has not been considered. The results have been obtained as contrast modulation in the image of a spatial frequency component in the object. The effect of polychromaticity in the recording beam is seen to be more severe than that due to the polychromaticity in the reconstruction beam. Fourier-transform holography seems to yield a better image. With the lensless Fourier-transform hologram recorded on monochromatic light, white light reconstruction seems to be possible if the illuminating beam is suitably dispersed before it falls on the hologram.     

Extreme-ultraviolet lensless Fourier-transform holography

We demonstrate 100-nm-resolution holographic aerial image monitoring based on lensless Fourier-transform holography at extreme-UV (EUV) wavelengths, using synchrotron-based illumination. This method can be used to monitor the coherent imaging performance of EUV lithographic optical systems. The system has been implemented in the EUV phase-shifting point-diffraction interferometer recently developed at Lawrence Berkeley National Laboratory. Here we introduce the idea of the holographic aerial image-recording technique and present imaging performance characterization results for a 10x Schwarzschild objective, a prototype EUV lithographic optic. The results are compared with simulations, and good agreement is obtained. Various object patterns, including phase-shift-enhanced patterns, have been studied. Finally, the application of the holographic aerial image-recording technique to EUV multilayer mask-blank defect characterization is discussed.     

Three-dimensional Displacement Analysis by Windowed Phase-shifting Digital Holographic Interferometry

Abstract:  Phase-shifting digital holography is a new method for measuring the displacement distribution on the surface of an object. The authors previously proposed a windowed phase-shifting digital holographic interferometry (windowed PSDHI). This method provides accurate displacement distributions by decreasing the effect of speckle patterns. In this study, the method is extended to analyse three-dimensional displacement components in a microscope. Three object laser beams in the optical system are used. Four phase-shifted holograms are recorded for each object laser beam. The complex amplitude of each reconstructed light at the object is calculated by the Fresnel diffraction integral of the complex amplitude of the hologram. The reconstructed distance is obtained at the point with the maximum of the standard deviation of the intensities of the object reconstructed with changing the reconstruction distance. The three phase-difference values between before and after deformation provide the three-dimensional displacement components. Theoretical treatment and experimental results of three-dimensional displacement measurement using this method are shown.     

Fresnel transform phase retrieval from magnitude

This report presents a generalized projection method for recovering the phase of a finite support, two-dimensional signal from knowledge of its magnitude in the spatial position and Fresnel transform domains. We establish the uniqueness of sampled monochromatic scalar field phase given Fresnel transform magnitude and finite region of support constraints for complex signals. We derive an optimally relaxed version of the algorithm resulting in a significant reduction in the number of iterations needed to obtain useful results. An advantage of using the Fresnel transform (as opposed to Fourier) for measurement is that the shift-invariance of the transform operator implies retention of object location information in the transformed image magnitude. As a practical application in the context of ultrasound beam measurement we discuss the determination of small optical phase shifts from near field optical intensity distributions. Experimental data are used to reconstruct the phase shape of an optical field immediately after propagating through a wide bandwidth ultrasonic pulse. The phase of each point on the optical wavefront is proportional to the ray sum of pressure through the ultrasound pulse (assuming low ultrasonic intensity). An entire pressure field was reconstructed in three dimensions and compared with a calibrated hydrophone measurement. The comparison is excellent, demonstrating that the phase retrieval is quantitative.     

Aberration compensation of holographic particle images using digital holographic microscopy

Characterisation of small and large-scale vortices in turbulent flows demands a system with high spatial resolution. The measurement of high spatial resolution, three-dimensional vector displacements in fluid mechanics using holography, is usually hampered by aberration. Aberration poses some problems in particle image identification due to low fidelity of real image reconstruction. Phase mismatch between the recording and the reconstruction waves was identified as the main source of aberration in this study. This paper demonstrates how aberration compensation can be achieved by cross-correlating the complex amplitude of an aberrated reconstructed object with the phase conjugate of a known reference object in the plane of the hologram (frequency space). Results favourably show significant increase in Strehl ratio and suppression of background noise that are more pronounced for particle images of 10 and 5 microns. It is clear from the work conducted that wavefront aberration measurement and compensation of holographic microscopic objects are now possible with the use of a variant digital holographic microscope.     

Some Effects of Spatial and Temporal Coherence in Holography

The following two problems have been investigated theoretically: systematic treatment of image formation in two-beam Fresnel holography from the viewpoint of spatial coherence, and influence of temporal coherence in two-beam Fraunhofer holography.     

Remote metrology by comparative digital holography

A method for the remote comparison of objects with regard to their shape or response to a load is presented. The method allows interferometric sensitivity for comparing objects with different microstructure. In contrast to the well-known incoherent techniques based on inverse fringe projection this new approach uses the coherent optical wave field of the master object as a mask for the illumination of the sample object. The coherent mask is created by digital holography to allow instant access to the complete optical information of the master object at any place desired. The mask is reconstructed by a spatial light modulator (SLM). The optical reconstruction of digital holograms with SLM technology allows modification of reconstructed wavefronts with respect to improvement of image quality, the skilled introduction of additional information about the object (augmented reality), and the alignment of the master and test object.     

Free-viewpoint images captured using phase-shifting synthetic aperture digital holography

Free-viewpoint images obtained from phase-shifting synthetic aperture digital holography are given for scenes that include multiple objects and a concave object. The synthetic aperture technique is used to enlarge the effective sensor size and to make it possible to widen the range of changing perspective in the numerical reconstruction. The lensless Fourier setup and its aliasing-free zone are used to avoid aliasing errors arising at the sensor edge and to overcome a common problem in digital holography, namely, a narrow field of view. A change of viewpoint is realized by a double numerical propagation and by clipping the wave field by a given pupil. The computational complexity for calculating an image in the given perspective from the base complex-valued image is estimated at a double fast Fourier transform. The experimental results illustrate the natural change of appearance in cases of both multiple objects and a concave object.     

Wavefront divergence: A source of error in quantified speckle shearing data

Abstract

Divergent laser illumination is commonly used in current designs of commercial electronic speckle pattern shearing interferometry (ESPSI) or shearography, for qualitative non-destructive testing (NDT) of material defects. The growing demand for quantitative out-of-plane (OOP) and more recently in-plane (IP) ESPSI, is determining the quality of optical system design and analysis software. However, little attention is currently being given to understanding, quantifying and compensating for the numerous error sources. Data describing the measurement inaccuracy due to the divergence of the object illumination wavefront for an OOP interferometer is presented. The errors are measured by comparing divergent object illumination with collimated illumination, with respect to illumination angle, lateral shear and shearing direction. Results indicate that the magnitude of the relative error increases by approximately a power function as the distance from the illumination source decreases.     

Fast acquisition system for digital holograms and image processing for three-dimensional display with data manipulation

A three-dimensional (3D) digital holographic display system with image processing is presented. By use of phase-shifting digital holography, we obtain the complex amplitude of a 3D object at a recording plane. Image processing techniques are introduced to improve the quality of the reconstructed 3D object or manipulate 3D objects for elimination and addition of information by modifying the complex amplitude. The results show that the information processing is effective in such manipulations of 3D objects. We also show a fast recording system of 3D objects based on phase-shifting digital holography for display with image processing. The acquisition of 3D object information at 500 Hz is demonstrated experimentally.     

Space-bandwidth conditions for efficient phase-shifting digital holographic microscopy

Microscopy by holographic means is attractive because it permits true three-dimensional (3D) visualization and 3D display of the objects. We investigate the necessary condition on the object size and spatial bandwidth for complete 3D microscopic imaging with phase-shifting digital holography with various common arrangements. The cases for which a Fresnel holographic arrangement is sufficient and those for which object magnification is necessary are defined. Limitations set by digital sensors are analyzed in the Wigner domain. The trade-offs between the various holographic arrangements in terms of conditions on the object size and bandwidth, recording conditions required for complete representation, and complexity are discussed.     

Digital in-line holography in thick optical systems: application to visualization in pipes

We apply digital in-line holography to image opaque objects through a thick plano-concave pipe. Opaque fibers and opaque particles are considered. Analytical expression of the intensity distribution in the CCD sensor plane is derived using a generalized Fresnel transform. The proposed model has the ability to deal with various pipe shapes and thicknesses and compensates for the lack of versatility of classical digital in-line holography models. Holograms obtained with a 12 mm thick plano-concave pipe are then reconstructed using a fractional Fourier transform. This method allows us to get rid of astigmatism. Numerical and experimental results are presented.     

Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene

We describe various techniques to synthesize three types of computer-generated hologram (CGH): the Fresnel-Fourier CGH, the Fresnel CGH, and the image CGH. These holograms are synthesized by fusing multiple perspective views of a computer-generated scene. An initial hologram is generated in the computer as a Fourier hologram. Then it can be converted to either a Fresnel or an image hologram by computing the desired wave propagation and imitating an interference process of optical holography. By illuminating the CGH, a 3D image of the objects is constructed. Computer simulations and experimental results underline the performance of the suggested techniques.