J. Eur. Opt. Society-Rapid Publ. 2026, 22, 14 Ó The Author( s), published by EDP Sciences, 2026 https:// doi. org / 10.1051 / jeos / 2026004 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Single shot sub-micron lensless digital holographic microscopy
André F. Battling 1, 2, *
, Justin A. Bich 2, Ralf B. Bergmann 1, 2, and Claas Falldorf 1, 2
1 University of Bremen, MAPEX Center for Materials and Processes and Faculty of Physics and Electrical Engineering, Otto-Hahn-Allee 1, 28359 Bremen, Germany 2 BIAS-Bremer Institut für angewandte Strahltechnik, Klagenfurter Str. 5, 28359 Bremen, Germany
Received 23 October 2025 / Accepted 14 January 2026
Abstract. High-resolution lensless microscopy offers a compact and cost-effective alternative to traditional optical microscopy, with various applications such as biomedical imaging and wafer-level testing. This paper introduces a model-based understanding of how to exploit the physical properties of the wave field despite the limited sampling capabilities of digital cameras, providing insights into the true resolution potential of lensless holographic imaging systems. Through the inversion of the propagation operator between two differently scaled sampling grids in the camera and object planes, we present a diffraction-limited imaging approach using a single digital hologram. We validate the method through both single-shot as well as temporally phase-shifted measurements and demonstrate lensless sub-micron imaging in both reflection and transmission mode.
Keywords: Lensless imaging, Lensless microscopy, Digital holography, Wave field propagation.
1 Introduction
Digital holography is a versatile imaging technique that enables the recording and reconstruction of threedimensional wavefronts. By utilizing the principles of interference and diffraction, it allows for the simultaneous capture of both the amplitude and phase information of light waves scattered from an object [ 1 ]. Unlike conventional optical imaging methods, digital holography eliminates the need for complex optical components while offering distinct advantages such as extended depth of field, volumetric imaging, and high-precision optical path measurement at the nanometer scale [ 2 ]. These unique capabilities make it widely applicable in fields such as metrology [ 3, 4 ], biomedical imaging [ 5 ], and holographic displays [ 6, 7 ]. Among these applications, lensless holographic microscopy has gained significant attention due to its potential to serve as a compact and cost-effective alternative to traditional lens-based microscopy [ 8, 9 ].
Recent advancements in image sensor technology, computational power, and reconstruction algorithms have further propelled the development of lensless holographic microscopy, making it an attractive solution for highresolution, depth-resolved imaging [ 10, 11 ]. By eliminating the need for bulky and expensive microscope objectives, lensless microscopy offers a portable and scalable approach for a wide range of applications, including biomedical diagnostics and environmental monitoring [ 12 ]. However,
* Corresponding author: abattling @ bias. de a well-known challenge in lensless holography, especially for on-chip methods, is the apparent resolution limit imposed by the pixel pitch of the camera sensor [ 13 ].
A common strategy to surpass the resolution constraints of the sensor is the implementation of pixel super-resolution techniques [ 14 ], which synthesise high-resolution holograms by combining multiple lower-resolution measurements [ 15 ]. This is typically achieved by recording multiple holograms while scanning the camera sensor [ 16 ], shifting the object [ 17 ], modifying the illumination [ 18 ], or introducing tunable diffraction gratings between the sample and the camera [ 19 ]. However, these approaches impose strict limitations on the study of dynamic or transient processes, as they require multiple sequential exposures.
To address the limitation of the finite pixel pitch for single shot measurements numerically, various computational reconstruction methods have been explored. Some approaches apply variable magnification on different pixel grids [ 20 ], allowing for the enhancement of features below the sensor’ s pixel pitch [ 21 ]. However, these methods often rely on approximations that assume low numerical apertures, which can constrain their effectiveness in highresolution lensless microscopy [ 22 ]. For far field measurements, the pixel grid can also be transformed for the reconstruction of objects that exceed the sensor size [ 23 ]. The scalable angular spectrum algorithm [ 24 ] realizes such a far field propagation method by utilizing the inherent pixel size transformation of the Fresnel propagation while pre-compensating for approximation errors of each spatial frequency due to the Fresnel approximations. This results
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