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J. Eur. Opt. Society-Rapid Publ. 22, 14( 2026)
Fig. 5. USAF resolution target measured by means of lensless holographic microscopy in transmission mode: The field of view is approx. 7 7mm 2, whereas the resolution is approx. 1.5 lm at group 8 element 3 as shown in the blow up. The image therefore has a remarkably high space-bandwidth product of more than 20 million.
Using a standard office computer with an Intel Core i7-5960X CPU, 3.00 GHz, the runtime of scenario realistic for industrial operation( N = 4512, q = 4) takes 35 s. For potential real-time operation, however computation times in the ls to ms range are ideal, a first step would be the implementation of the algorithm on a modern GPU.
3 Experimental results
3.1 Setup
As described above, to experimentally implement the proposed scheme for single shot sub-micron lensless microscopy a lensless Fourier holographic setup with a known reference wave is necessary. To allow for the wave field to be completely sampled, including all its high-frequent features necessary for full resolution, we consequently use a spherical reference wave with its origin approximately at the objects distance from the target.
We realized this in several setups both in transmission and reflection mode. Figures 4a, 4b show the main components as well as the light paths in transmission and reflection mode respectively. The reference source point is positioned slightly off-axis to allow for spatial phase shifting. In the reflection mode setup shown in Figure 4b the object illumination is generated by a lens, placed directly in front of the beam splitter. The reference source points for both transmission and reflection can be realized in multiple ways, e. g., using pinholes, tapered fiber tips( with high numerical aperture around NA 0.5) or by using microscope objectives to generate small focus points. In the following we demonstrate the technique both using tapered fiber tips as well as microscope objectives. Note that the term“ lensless microscopy” here denotes the absence of lenses between object and camera. The utilized lenses are only used for beam shaping and do not directly influence the imaging or the resolution of the reconstruction.
All measurements shown below were recorded with exposure times in or below the single digit ms range, making the single-shot measurement robust against mechanical vibrations. The camera gain was set to zero. Objects were positioned manually via micrometer precision stages.
For off-axis measurements the temporal coherence length of the utilized lasers had to be at least in range of 500 lm to realize a modulation of the hologram with a spatial carrier frequency across the whole camera plane. The spatial coherence length has to be as large as the camera width, for fully modulated holograms. This can be realized by adjusting the choice of reference and object illumination source points described above.
The more detailed setup for transmission is shown in Figure 4c for measurements of e. g., biological samples and is based on a Mach – Zehnder-interferometer. The wave field from a fiber coupled laser is divided using a 50 / 50 fiber splitter( Thorlabs TW630R5F2) and recombined through a beam splitter after the object wave is diffracted by the object. Additionally, polarization filters are placed in both the object illumination and the reference arm of the interferometer to avoid degradation due to mismatched polarization. Potential degradations due to glare are effectively minimized by the use of diverging point sources. Problems due to reflections and ghost imaging caused by the beam splitter can be circumvented by using spatial phase shifting and masking the measured cross-term in Fourier-space. Therefore, no anti-reflective coating for the beam splitter is necessary.
In Figure 5 we see an example of a lensless microscopic image of a USAF resolution test chart in transmission. We used a CMOS camera with a Sony IMX661 sensor, containing 13376 times 9528 pixels with a pitch of 3.45 lm, a frequency-double Nd: YAG laser at k = 532 nm, and a beam splitter cube with 50 mm side lengths. The point sources were generated using microscope objectives. The field of view is approx. 7 7mm 2 and from the detail we see that the resolution is approx. 1.5 lm( group 8, 3rd element), well below the pixel pitch. This corresponds to diffraction limited imaging with a numerical aperture of N A = 0.25 over a comparably large field of view. The space bandwidth-product( SBP) of the image is more than 20 million, which is remarkable considering that typical microscope objectives achieve SBPs between 9 and 15 million.
For even lower resolutions around the diffraction limit, a high signal-to-noise ratio is paramount. One way to achieve higher signal-to-noise ratios is to place the source point of the object illumination close to the object itself,