High-Resolution Large-Depth-Range Digital holography for 3D Optical Metrology

Abstract

Digital holography (DH) is a full-field, three-dimensional optical imaging technique for high-speed industrial inspection. By retrieving the complex optical field, DH provides quantitative phase information that enables three-dimensional measurement of surface topography. This thesis is motivated by the demands of advanced semiconductor manufacturing and assembly, where centimeter-scale depth ranges and large field-of-views must be achieved at high throughput. A lensless configuration is used to keep the optical system compact and integration-friendly, while numerical propagation enables refocusing. Within this framework, three key challenges of DH-based metrology are addressed: limited unambiguous depth range due to phase wrapping, pixel-size-limited lateral resolution in lensless DH configurations, and the trade-off between depth range and depth precision.

Industrial samples often exhibit large and abrupt height variations. In singlewavelength DH, the unambiguous depth range of half a wavelength is insufficient to unambiguously determine the height of micrometer to millimeter-scale structures. Chapter 2 describes the development of a dual-wavelength off-axis lensless DH configuration with spatial-frequency multiplexing to enable single-shot acquisition at two discrete wavelengths. By leveraging the beat frequency of the two wavelengths, the system generates a synthetic wavelength, which extends the unambiguous depth range to half the synthetic wavelength. A model for shot-noiselimited phase-precision is derived and experimentally validated. Measurements on calibrated targets and representative industrial samples demonstrate reliable threedimensional reconstruction over extended depth ranges, confirming the suitability of single-shot dual-wavelength DH for high-speed metrology.

When DH is implemented in a lensless configurations, the lateral resolution is constrained by sensor pixel size, which limits the maximum spatial frequencies and thus restricts the detection of fine features such as micro-defects. To overcome this limitation, Chapter 3 introduces an expanding wavefront illumination scheme that increases the available angular spectrum of the object field while maintaining system compactness. A background aberration compensation algorithm is developed to correct global aberrations using locally sampled regions, thereby retaining singleshot operation. By incorporating a tunable external-cavity diode laser, the system achieves a centimeter-scale depth range in combination with micrometer-scale lateral resolution.

Besides a large depth range, industrial metrology also demands high depth precision over the accessible depth span. In conventional dual-wavelength DH, increasing the synthetic wavelength enlarges the unambiguous range but proportionally amplifies phase noise when converted to height, which leads to degraded precision. Chapter 4 addresses this trade-off by developing a multi-wavelength DH technique based on discrete wavelength sampling. In multi-wavelength DH, the surface height is retrieved via multi-point phase fitting in the wavenumber domain, thereby combining Fourier-based coarse depth localization with linear regression. The utilized self-calibration strategy, based on pairwise beat-phase analysis, removes the need for auxiliary high-precision wavelength-monitoring instruments. This approach mitigates noise amplification and improves depth precision over a large depth range, broadening the feasibility of DH for large-scale, high-precision industrial inspection.

In summary, this thesis demonstrates that coordinated advances in optical system design and computational reconstruction can alleviate key limitations of DH in industrial metrology. By extending the depth range, enhancing lateral resolution, and improving depth precision, the proposed methods broaden the applicability of DH while maintaining its intrinsic advantages of full-field imaging and quantitative phase retrieval.