We can efficiently use digital holographic microscopy for monitoring of sparse samples. From a recorded hologram the whole illuminated volume can be reconstructed using numerical simulation of wave propagation. From a single recorded hologram we can reconstruct several objects at different depths within the volume. Thus we can avoid the small depth of field constraint of conventional microscopes, and even 200 times larger volume can be observed from a single exposure. For this purpose so far we applied Gabor type in-line hologram recording architecture, where the illuminating coherent light source provides the reference. This architecture offers a simple, robust measuring setup that is relatively insensitive against vibrations and it is easy to satisfy the coherence length requirements of the applied light source. It is easy to solve the hologram recordings, but of the numerically reconstructed image of the objects are always contaminated by the diffractions of the so called zero order and twin image terms. The phase retrieval that can remove these biases, and reconstruct the shape and refractive index distribution of the objects can be fulfilled by some slow iterative algorithms. Several numerical methods have been introduced so far to solve this phase retrieval task. Unfortunately, the convergence speed of these algorithms is really low, especially in the case of systems of high Fresnel number, and this way usually only incomplete reconstructions can be accomplished.
To overcome this limitation of the in-line systems, Leith and Upatnieks introduced the off-axis hologram recording architecture. In this setup, an appropriately tilted reference beam is applied. The tilted reference can be considered as a carrier wave modulation of the object wave field. This way, by the application of proper spatial frequency filtering the object term is separable from the zero order and conjugate object terms. However, this filtering considerably limits the bandwidth of the reconstruction. To achieve large resolution object reconstructions, appropriate optical magnification has to be applied before recording the hologram that in turn compromises the reachable field of view. Anyway the fast phase reconstruction limits the applicable space-bandwidth product. This is one of the main drawbacks of this setup. There has been made attempts that were able to partially ameliorate this pitfall using smart optical arrangements. From the achievable resolution point of view the application of an in-line setup is preferred.
There are eloquent numerical phase reconstruction techniques, where special regularization terms are applied to retrieve the phase of the object from one or more measured holograms. However, these techniques require large number of iterations and the applied regularization constraints the amplitude and phase distribution of the reconstructions. Alternative measuring techniques were also introduced to ensure the exact reconstruction of the object wave field without the resolution compromise of the off-axis systems. All these methods, like the phase-shifting interferometry, phase diversity based methods, transport of intensity algorithms, or aperture synthesis based techniques, require the recording of several holograms. Accordingly, they are not applicable, when moving objects are to be measured. Furthermore, these methods require complex measuring setups with intricate and expensive additional devices (e.g. implementing the required phase shifts), and usually demands accurate adjustment and precise calibration of the components.
Furthermore, as several hologram recording step are required for the phase retrieval they are not applicable for the measurement of moving, rapidly changing samples.
Earlier the in-line and off-axis hologram recording architecture was used as alternative of one another. Either it provides a simple measuring device, but the reconstruction is biased or the phase retrieval is complicated, or the measuring device is more complex, but the reconstruction is straightforward and the field of view is small.
We have recognized that is special circumstances, especially in the case of sparse samples, the off-axis hologram zero order terms include the in-line hologram too. Using this fact, earlier we have found a method that speed up the in-line hologram phase retrieval. However, we need an off-axis and an in-line hologram. This method is based on that by these of the object term of the off-axis hologram we can correctly reconstruct of the hologram small spatial frequencies of the in-line hologram, while the phase retrieval algorithm of the in-line hologram can reconstruct the high spatial frequencies much easier.
Márton Zsolt Kiss