In practice, the wrapped phase in interferometry is often affected by noise and discontinuity, and among the various types of phase unwrapping (PU) method, the weighted least-square (WLS) PU algorithm, as a global strategy, is widely utilized. However, the excessive smoothing effect exists within the process of PU. Therefore, it is necessary to conduct a comprehensively analysis of different WLS PU algorithms, which includes noise resistance, discontinuity characteristics, convergence speed, and accuracy. First, different weighting strategies were compared with detail for the WLS approach. Under slight noise condition, the edge detection map (EDM) and the filtering method both obtained relatively accurate and reliable phase information. However, when it comes to global multiplicative noise such as speckle noise, the filtering method showed better anti-noise performance than the EDM method, whereas EDM was more capable of dealing with discontinuous phase. Second, to improve the iterative convergence speed and accuracy, the initial value selection was analyzed in detail, and a new initial value selection method was proposed. Simulation and experiments were carried out and validated the results of the analysis.
A telephoto structure-based laser autocollimation with common-path compensation method is proposed to compensate laser beam drift of laser autocollimator. According to the analysis, the measurement beam and the reference beam propagate alongside nearly the same path with approximately identical amounts of drift. Moreover, the ellipses fitting algorithm based on least square approach ensures the accuracy of extracting centroid of the beam while the only photodetector (CCD) with the telephoto objective and several reflectors guarantees the compaction and effectiveness of the system. Simulations and experiments demonstrate a significant beam drift compensation result up to 86.5%. In other words, the stability of the laser beam in the process of measurement is improved.
Digital holographic microscope (DHM) as a quantitative phase imaging and surface metrological tool for microstructure objects has shown increased interest over the past two decades. In this paper, we report the development of two commercial digital holographic microscopes (reflection mode and transmission mode) for different applications. The two microscopes all use a CCD camera for recording of a digital off-axis hologram and a numerical method for reconstructing the hologram. The user-friendly software simultaneously provides an amplitude image and a quantitative phase image of the object. Furthermore, additional features include various image enhancements, cross-sectional and line profiling, measurement and data analysis tools. Some applications of the two products are presented on different specimens, such as MEMS, cells.
An improved compact digital holographic microscope (ICDHM) is developed for three-dimensional imaging of microstructures. This system is based on lensless magnification using a diverging wave. A point source generated by a long working distance microscope objective is located into the cube beam-splitter to get a higher numerical aperture (NA) of the system. The lateral resolution and the field-of-view of the system are confirmed with a calibration experiment. For the case of the optical path lengths (OPL) of object with step pattern larger than the wavelength, the traditional phase unwrapping algorithms cannot be unequivocally determinate, resulting in a 2π phase ambiguity. To solve this problem, dual wavelength phase unwrapping method was integrated into ICDHM, which extends the measuring capability of ICDHM over several microns of range. The experimental results demonstrate that the developed system is well suitable for the measurement of MEMS and Micro systems samples with high resolution.
Wafer-level-optics now is widely used in smart phone camera, mobile video conferencing or in medical equipment that require tiny cameras. Extracting quantitative phase information has received increased interest in order to quantify the quality of manufactured wafer-level-optics, detect defective devices before packaging, and provide feedback for manufacturing process control, all at the wafer-level for high-throughput microfabrication. We demonstrate two phase imaging methods, digital holographic microscopy (DHM) and Transport-of-Intensity Equation (TIE) to measure the phase of the wafer-level lenses. DHM is a laser-based interferometric method based on interference of two wavefronts. It can perform a phase measurement in a single shot. While a minimum of two measurements of the spatial intensity of the optical wave in closely spaced planes perpendicular to the direction of propagation are needed to do the direct phase retrieval by solving a second-order differential equation, i.e., with a non-iterative deterministic algorithm from intensity measurements using the Transport-of-Intensity Equation (TIE). But TIE is a non-interferometric method, thus can be applied to partial-coherence light. We demonstrated the capability and disability for the two phase measurement methods for wafer-level optics inspection.
Transport-of-intensity equation (TIE) is an effective method for the quantitative phase analysis. Comparing with other quantitative phase imaging methods, TIE is dynamic, non-laser, and vibration insensitive. Based on the TIE technique, we designed and developed a system, including a phase quantitative imaging device and an application software, for real-time measurement of dynamic samples. In this paper, the structures of the system, especially the structure of the application software, are described. The performance and usage examples of the system are also demonstrated.
Digital holography microscopy (DHM) allows fast, nondestructive, high resolution and full-field 3D shape measurement of micro-objects. However, a drawback of many experimental arrangements of DHM is the requirement for a separate reference wave, which results in a measurement stability and interference fringe contrast decrease. In this paper, a common-path DHM (CDHM) is explored which only requires a single object illumination wave. Due to the fact that conventional phase unwrapping algorithms are not suitable for the complex and step surface of object, the dual wavelength linear regression phase unwrapping algorithm is introduced. By comparing two wrapped phase maps reconstructed at different wavelengths, the maps can be accurately unwrapped with straightforward and less timeconsuming. From the CDHM system and the phase unwrapping algorithm introduced, we experimentally obtained high quality depth profiles of micro-objects.
This paper discusses conventional synthetic-aperture method combined angular multiplexing in digital holography to increase the resolution and to enlarge the field of view at the same time. A structured illumination is used to realize angular multiplexing. A camera is moved by a motorized x-y stage, and scanning is performed at imaging plane. In this way we extend the band-pass for single hologram recording as well as obtain a greater sensor area resulting in a larger numerical aperture (NA). A larger NA enables a more detailed reconstruction combined with a smaller depth of field. Moreover, a phase map of the object is experimentally presented.
Phase unwrapping is a process to reconstruct the absolute phase from a wrapped phase map whose range is (−π, π]. As the absolute phase cannot be directly extracted from the fringe pattern, phase unwrapping is therefore required by phasemeasure techniques. Currently, many phase unwrapping algorithms have been proposed. In this paper, four popular phase unwrapping algorithms, including the Goldstein’s branch cut method, the quality-guided method, the Phase Unwrapping via Max Flow (PUMA) method, and the phase estimation using adaptive regularization based on local smoothing method (PERALS), are reviewed and discussed. Detailed accuracy comparisons of these methods are provided as well.
In the compact digital holoscope (CDH) measurement process, theoretically, we need to ensure the distances between the reference wave and object wave to the hologram plane exactly match. However, it is not easy to realize in practice due to the human factors. This can lead to a phase error in the reconstruction result. In this paper, the strict theoretical analysis of the wavefront interference is performed to demonstrate the mathematical model of the phase error and then a phase errors elimination method is proposed based on the advanced mathematical model, which has a more explicit physical meaning. Experiments are carried out to verify the performance of the presented method and the results indicate that it is effective and allows the operator can make operation more flexible.
In this paper we present a new method to compensate for phase aberrations and image distortion with recording single digital hologram in digital holographic microscopy. In our method, tilt is removed from the abberrated phase map first. Then an area of interest (AOI) is generated by flood filled algorithm. By fitting AOI with discrete orthogonal Zernike polynomials, error phase map in the form of a series of Zernike polynomials is obtained. Final result can be calculated by subtracting the error phase map from the abberrated phase map. Through applying our method in microlens testing, phase aberrations and image distortion introduced by microscope objective are well suppressed.
A compact reflection digital holographic microscopy (DHM) system integrated with the light source and optical interferometer is developed for 3D topographic characterization and real-time dynamic inspection for Microelectromechanical systems (MEMS). Capability enhancement methods in lateral resolution, axial resolving range and large field of view for the compact DHM system are presented. To enhance the lateral resolution, the numerical aperture of a reflection DHM system is analyzed and optimum designed. To enhance the axial resolving range, dual wavelengths are used to extend the measuring range. To enable the large field of view, stitching of the measurement results is developed in the user-friendly software. Results from surfaces structures on silicon wafer, micro-optics on fused silica and dynamic inspection of MEMS structures demonstrate applications of this compact reflection digital holographic microscope for technical inspection in material science.
The determination of numerical reconstruction distance is key to recover the wavefront at focal plane in digital holography. In this paper, we propose a new autofocus method based on angular spectrum method (ASM). The proposed method takes successive Fourier transform after 1st order spectrum selection, and then calculates the summation. It saves operations compared to classic autofocus functions. When an exhaustive z-axis search is performed, the proposed method obtains unimodality coincided with the results from four classic autofocus functions. Moreover, the proposed method is more time-effective, which is the optimal one for ASM.
An off-axis annular subaperture stitching interferometry (OASSI) is presented to test off-axis aspheric surfaces. In view of this, the relationship between misalignment and wavefront aberration is deduced with a strict theoretical analysis. The analytic result shows that the relative misalignment errors between the interferometer and the off-axis mirror tested will lead to complex wavefront aberrations in the measurement result other than the ordinary terms of piston, tilts, and power. Based on the analytic result, a suitable off-axis stitching algorithm is developed for stitching the off-axis subaperture. Both the numerical simulations and preliminary experimental results prove the potential of the proposed approach for the measurement of off-axis aspheric surfaces. As far as we know, this is the first time that OASSI has been used to test the off-axis aspheric surface.
A simple and effective automatic positioning method (APM) is proposed for the application of annular subaperture stitching interferometry in the stage of precision polishing. In the testing process, a series of optical path difference (OPD) data of subaperture are obtained since the interferometer is shifted relative to the tested aspheric surface. These OPD data are analyzed by the APM to get the key stitching parameters (e.g., aspheric departure) without a precision motion system. The basic principles of the APM are described. The performance of the method is simulated in some pertinent cases. Finally, we study the applicability of the proposed method to subaperture stitching tests of a hyperbolic mirror. The stitching results agree with the full-aperture test results. It demonstrates the validity and practicability of the proposed algorithm.
Annular subaperture stitching interferometry (ASSI) is increasingly used for precision metrology of aspheric surfaces. The stitching model is a critical factor for stitching algorithms in ASSI. An optimized stitching model is proposed, which describes the alignment errors of adjacent subapertures based on an off-axis model and wave aberration theory. To keep the stitching errors from transmitting and accumulating, a simultaneous optimization algorithm is presented. The residual difference of overlapped regions of adjacent subapertures is utilized to evaluate the stitching accuracy. Finally, the comparative numerical simulations and experiments are carried out. It shows that the optimized stitching model has a better performance and validity.
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