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J. Eur. Opt. Society-Rapid Publ. 22, 15( 2026)
Figure 4. a) The test object is a stainless steel spring with diameter of 4.3 ± 0.1 mm, a depth of L = 26 ± 0.1 mm and a thread pitch of approx. 2 mm. b) Digital-holographic hypercentric reconstruction of the object with an aperture of d = 1.5 mm, featuring a visible object depth of approx. 4 mm. The insert shows an image of the top of the object. This ability to refocus to arbitrary perspective planes parallel to the sensor offers the possibility to extend the depth of field by numerical refocusing, although in this case the hypercentricity as given by equation( 6), is changed with different z P, which has to be considered. Consequently, in order to keep the hypercentricity constant the aperture plane would have to be adjusted accordingly for a constant z P. In a lens-based system, this would need mechanical adjustment of the focus position by axially shifting the objective. However, for our lensless approach this can be implemented with no great effort, as an exact adaptation of the virtual aperture position is possible at any time.
For further demonstration of the lensless hypercentric imaging, a stainless steel spring with a diameter of 4.3 ± 0.1 mm, a depth of L = 26 ± 0.1mmandathread pitch of approx. 2 mm was used, as shown in Figure 4a. In this case, the hypercentric perspective is realized using a centered aperture with d = 1.5 mm and an aperture plane at distance z P = 12 mm from the perspective plane, which was chosen 1 mm below the top surface. The result is shown in Figure 4b and features a visible object depth of approx. 4 mm. These results prove the feasibility of digitalholographic hypercentric reconstruction and open completely new opportunities for the implementation and application of the hypercentric imaging process.
4 Conclusion
In this work, we have presented a novel approach for implementing hypercentric imaging on the basis of lensless digital holography. The imaging translates into the hypercentric imaging modality by applying a virtual aperture in the numerical reconstruction of the hologram. We developed a theoretical model describing the digital hypercentric imaging including all relevant parameters and tested it in experiment. Here, we demonstrated the feasibility of our new method by achieving highly resolved hypercentric perspectives on the object and showed how the imaging is affected by the positioning and sizing of the virtual aperture in axial and lateral dimensions. Moreover, we have shown that our theoretical model correctly predicts the level of hypercentricity, measured by the perspective spread, whereby a geometric model for this imaging modality is successfully established. It should be noted that our treatise is limited to the realm of scalar diffraction theory. Very large numerical apertures in the recording scheme and highly oblique propagation directions may require further extension towards vectorial optics.
The purpose and the main novelty of this work is the introduction of a lensless hypercentric imaging based on digital holography. Therefore, at the moment, the given examples mainly focus on qualitative imaging in order to introduce and demonstrate the lensless imaging functionality and to describe its main governing parameters. However, in future work this method can be expanded into all areas where hypercentric imaging is beneficial, especially in industrial inspection and in optical metrology. Embedded in the framework of lensless digital holography and its advantages like numerical refocusing and freely adaptable virtual apertures, the hypercentric imaging modality offers great potential for interferometric inspection applications.
Funding
This work was funded by the German Research Foundation( Deutsche Forschungsgemeinschaft, DFG) under the project: Hypercentric Imaging in Coherent Optical Metrology,“ HyperCO- Met”( Project number 430572965).
Conflicts of interest There are no conflicts of interest.
Data availability statement
The underlying data is not publicly available at the time but can be provided by the authors upon reasonable request.