Resolving phase errors in microsphere assisted interferometry

Abstract

Microsphere assisted microscopy (MAM) has been rapidly developed to meet the measurement needs of microstructures. MAM can be integrated with optical interference microscopy (OIM) to achieve high lateral resolution surface profile measurement. However, the microspheres introduce intricate phase changes, resulting in optical path asymmetry which is very challenging to compensate for. This limitation constrains the application of MAM in OIM. In this paper, simulation analysis reveals that the phase transmission of the microsphere is influenced by parameters such as microsphere diameter and its relative position to the sample. It is concluded that a unique compensation process must be adopted for each individual microsphere. Addressing this issue, we proposed a phase compensation algorithm based on the three-dimensional position control of the microsphere and integrated it into our combined system of MAM and white light interferometry (WLI), reducing the phase errors introduced by the microspheres while enhancing the lateral resolution of optical system. This approach improved the profile measurement accuracy, offering a perspective for optically measuring the surface profile of intricate microstructures.

Keywords

microsphere assisted microscopy / microsphere assisted interferometry / optical interference microscopy / surface profile measurement / phase compensation

References

[1] YANG S, ZHANG G. A review of interferometry for geometric measurement. Measurement Science and Technology, 2018, 29(10): 102001.

[2] WANG Y, XIE F, MA S, et al. Review of surface profile measurement techniques based on optical interferometry. Optics and Lasers in Engineering, 2017, 93: 164.

[3] TANG M W, LIU X W, WEN Z, et al. Far-field superresolution imaging via spatial frequency modulation. Laser & Photonics Reviews, 2020, 14(11): 1900011.

[4] MICÓ V, ZHENG J J, GARCIA J, et al. Resolution enhancement in quantitative phase microscopy. Advances in Optics and Photonics, 2019, 11(1): 135.

[5] KIM M, CHOI Y, FANG-YEN C, et al. Three-dimensional differential interference contrast microscopy using synthetic aperture imaging. Journal of Biomedical Optics, 2012, 17(2): 026003.

[6] PATURZO M, MEROLA F, GRILLI S, et al. Super-resolution in digital holography by a two-dimensional dynamic phase grating. Optics Express, 2008, 16(21): 17107-17118.

[7] CHEN L W, ZHOU Y, LI Y, et al. Microsphere enhanced optical imaging and patterning: From physics to applications. Applied Physics Reviews, 2019, 6(2): 021304.

[8] ZHOU Y, TANG Y, DENG Q Y, et al. Contrast enhancement of microsphere-assisted super-resolution imaging in dark-field microscopy. Applied Physics Express, 2017, 10(8): 082501.

[9] ZHOU Y, TANG Y, HE Y, et al. Effects of immersion depth on super-resolution properties of index-different microsphere-assisted nanoimaging. Applied Physics Express, 2018, 11(3): 032501.

[10] WU G X, HONG M H. Optical microsphere nano-imaging: progress and challenges. Engineering, 2024, 36: 102-123.

[11] YAN B, WANG Z B, PARKER A L, et al. Superlensing microscope objective lens. Applied Optics, 2017, 56(11): 3142-3147.

[12] YAN B, SONG Y, YANG X B, et al. Unibody microscope objective tipped with a microsphere: design, fabrication, and application in subwavelength imaging. Applied Optics, 2020, 59(8): 2641-2648.

[13] WANG Z B, GUO W, LI L, et al. Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope. Nature Communications, 2011, 2: 218.

[14] CHEN L W, ZHOU Y, WU M X, et al. Remote-mode microsphere nano-imaging: new boundaries for optical microscopes. Opto-Electronic Advances, 2018, 1(1): 17000101-17000107.

[15] WU G X, ZHOU Y, HONG M H. Sub-50 nm optical imaging in ambient air with 10× objective lens enabled by hyper-hemi-microsphere. Light: Science & Applications, 2023, 12: 49.

[16] KWON S, PARK J, KIM K, et al. Microsphere-assisted, nanospot, non-destructive metrology for semiconductor devices. Light: Science & Applications, 2022, 11: 32.

[17] WANG Y X, GUO S, WANG D Y, et al. Resolution enhancement phase-contrast imaging by microsphere digital holography. Optics Communications, 2016, 366: 81-87.

[18] ABBASIAN V, GANJKHANI Y, AKHLAGHI E A, et al. Super-resolved microsphere-assisted Mirau digital holography by oblique illumination. Journal of Optics, 2018, 20(6): 065301.

[19] LIN Q W, WANG D Y, WANG Y X, et al. Super-resolution quantitative phase-contrast imaging by microsphere-based digital holographic microscopy. Optical Engineering, 2017, 56(3): 034116.

[20] ABBASIAN V, PAHL T, HÜSER L, et al. Microsphere-assisted quantitative phase microscopy: a review. Light: Advanced Manufacturing, 2024, 5(1): 133-152.

[21] DARAFSHEH A, ABBASIAN V. Dielectric microspheres enhance microscopy resolution mainly due to increasing the effective numerical aperture. Light: Science & Applications, 2023, 12: 17-19.

[22] LEONG-HOI A, HAIRAYE C, PERRIN S, et al. High resolution microsphere-assisted interference microscopy for 3D characterization of nanomaterials. Physica Status Solidi (a), 2018, 215(6): 1700858.

[23] PERRIN S, DONIE Y J, MONTGOMERY P, et al. Compensated microsphere-assisted interference microscopy. Physical Review Applied, 2020, 13: 014068.

[24] WANG F F, LIU L Q, YU H B, et al. Scanning superlens microscopy for non-invasive large field-of-view visible light nanoscale imaging. Nature Communications, 2016, 7: 13748.

[25] ZHOU J, LIAN Z X, ZHOU C J, et al. Scanning microsphere array optical microscope for efficient and large area super-resolution imaging. Journal of Optics, 2020, 22(10): 105602.

[26] MASLOV A V, ASTRATOV V N. Resolution and reciprocity in microspherical nanoscopy: point-spread function versus photonic nanojets. Physical Review Applied, 2019, 11(6): 064004.

[27] DUOCASTELLA M, TANTUSSI F, HADDADPOUR A, et al. Combination of scanning probe technology with photonic nanojets. Scientific Reports, 2017, 7: 3474.

[28] YANG H, TROUILLON R, HUSZKA G, et al. Super-resolution imaging of a dielectric microsphere is governed by the waist of its photonic nanojet. Nano Letters, 2016, 16(8): 4862-4870.